{"as_of":"2026-08-08T18:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3d0004d0e4107ab7fcf10e6c81edb500cd2fead94094c1c10a95e30dc481bb24","coverage":[{"denominator":42,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":42,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-27T08:23:45.294590Z","state":"measured"},{"denominator":42,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":42,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2606.11764/citation-record","integrity":"/paper/2606.11764/integrity","json":"/paper/2606.11764/citation-record.json","paper":"/paper/2606.11764"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Orthogonal Direct Sum Masking: A Smartcard Friendly Computation Paradigm in a Code, with Builtin Protection against Side-Channel and Fault Attacks,","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:c258ab0d48e689c826701e0fe3d560b9b3676bb4bb9e942c996d0a873d67d290","observation_id":"74ad4bbb-b74c-4a14-9abb-42a06924f3b7","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Complementary Dual Codes for Counter-Measures to Side-Channel Attacks,","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:5f876ce16dfeefda364f023ca7c2423c7698a5a4d8bd05e61436686dd7b56efc","observation_id":"c1675bec-63a6-478e-b73c-68faa93a2784","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Encoding the state of integrated circuits: A proactive and reactive protection against hardware Trojans horses,","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:4cffe3ee7a77bf265dec08df4f6a5852b42130ee70d1a055bea61a8ef857fe3d","observation_id":"e741621b-0cba-4bab-870f-ba7990331b41","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Linear complementary dual code improvement to strengthen encoded circuit against hardware Trojan horses,","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:716246c114433d8eeda9e95051a163305f73813f8549dafb791e32dcc2e9a73c","observation_id":"145b0b3c-c56a-4e1a-b20b-aa3a01b73e04","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Linear codes with complementary duals,","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:71ebd1bf4d36b1011367b42e6f2e87db0131f16d95c3a23b5d03012066733469","observation_id":"f041f511-7993-45b3-be60-90c0a27a9de5","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"The condition for a cyclic code to have a complementary dual,","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:4830ea9c0b770aeee82a8a9dc9124642d27148632a1820494ecde5528769bedb","observation_id":"cf3f192e-25ba-4d4f-b85e-52cc934d1ea4","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Linear Codes OverF q Are Equivalent to LCD Codes forq >3,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:41c537852be01e105ceee7e1396a3ca35fd76db9a5791a1680de1d56c7f46b6e","observation_id":"96a63533-571a-4e28-8bb8-931adec7800a","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Algebraic Geometry Codes With Complementary Duals Exceed the Asymptotic Gilbert-Varshamov Bound,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:8c86aeff796b397437a352c25ffcbc2fa614e6fc769ab7e51784103aada360e2","observation_id":"a0323c11-ce1f-4b6d-9f3c-e1e1a5857f2e","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"On Linear Complementary Pairs of Codes,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:c8b816e52deb81cf7bcb5682c7688f59489774d877c76bc468a4a47f70d3abb5","observation_id":"f7d24ac7-4759-4679-a4d0-98b950fc6cfb","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"On Linear Complementary Pair ofnD Cyclic Codes,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:be16652846bbb059c5ed84dbf2e0f2556b6c25c80c86a703f4c5378c595db629","observation_id":"6921569c-047f-4a8d-bc26-82d3d5281b92","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Linear codes with complementary duals meet the Gilbert–Varshamov bound,","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:27dfec4a68d397ac0175fe3a208184de68f252851ca0241a46147d9c2a25e9cc","observation_id":"d8b4b001-f038-48a9-9af3-84caa95abc18","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Euclidean and Hermitian LCD MDS codes,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:73858587bdbc71dee4af07b9344f4ace997e440629ed9bd8f391ec7c88513c8d","observation_id":"8a4466ed-4688-4ae7-bd9c-77ae284f8eb5","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Constructions of optimal LCD codes over large finite fields,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:10fa3ea85416fbf2f923e6d94164c9b7fe35e74f71574613b2c0c132aff5328d","observation_id":"59c6978a-8afa-46bf-adef-cff661184853","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Linear complementary pairs of codes over a finite non-commutative Frobenius ring,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:c5eb0077031c379a0c7973c2250560036ae08fb5335ac0e05aa704ed77562454","observation_id":"f4bcb51d-9b80-4789-9376-66a4d06ae9fe","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Several constructions of optimal LCD codes over small finite fields,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:1f91faf825bea3708767e384ad9a9bc6a259734f3dd5ac3af6ba6ee2f878c393","observation_id":"19a8ff4f-3150-4fe7-b62f-075c30b16d2e","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"A note on linear complementary pairs of group codes,","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:6b2b2543675dbf23a431c971e8a605e57ba4ca4f8e3f22728cdf63c832a2d6a0","observation_id":"e560696c-54d7-4ca4-b93e-779257b7b735","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Linear complementary pairs of codes over rings,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:9512cb584c9fa811e5c266159952de9fab084817abbb33323ccdca05fb555af2","observation_id":"54a45f9a-6c39-4d9c-9bb8-4a4051aa530c","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Construction for both self-dual codes and LCD codes,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:c11da6c3a1b3f499890b12af6dd3afc86c61a687ad0fd6f25045270c286d5dd4","observation_id":"b38c8412-539b-425a-bbbf-1ed552a570a0","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Construction of binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:d8b02ac1dc7452f679eb00230f066db20f8fbcfc847974b6519c53511e563d2e","observation_id":"40a615ae-0039-4fab-9b78-850c2ad40913","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"ALGEBRAICO-GEOMETRIC CODES,","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:f7d60e3a9f6e3a3fe1096004663f9b2c9b9a1b8ce11c22b3e50e7a8c53059822","observation_id":"b822536f-fe29-48b0-b51c-85fb2db279aa","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Explicit MDS Codes With Complementary Duals,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:4723fccf73d0c76d8b1ca50e4ea9ab5aaa35a84f72859febb51f057df306dad0","observation_id":"ee765f33-3d1e-48d1-b5a6-29fdbc18bbb2","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Complementary Dual Algebraic Geometry Codes,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:04b2e03da13a0ed35327253ec40d73943c574d0e06d38cef00ce5feb195c06a9","observation_id":"87b59806-d92c-4bbe-86ca-a044a346a6c6","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"On linear complementary pairs of algebraic geometry codes over finite fields,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:258d5a4f2ba76b6a69cbef06077b54700f4ceba6052088346c4d3048a67ab21f","observation_id":"9d352cf3-df10-4a81-bf6e-ea96abdfeb33","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Explicit Non-special Divisors of Small Degree, Algebraic Geometric Hulls, and LCD Codes from Kummer Extensions,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:e7be741488179808120a05176169ea323f564f4c3239370a4a545d0783d0d551","observation_id":"b0d4a1cf-46a0-4ec1-8c99-d7e6fae077ea","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Linear Complementary Dual Codes and Linear Complementary Pairs of AG Codes in Function Fields,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:56ae14c3f8fab2b42ef0d803f4e25b0bd666a3f4d36f7b6012be7331651aa339","observation_id":"217f25f8-84ff-4a7a-bac5-700301250052","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.23081","last_updated":"2025-06-29T04:21:05Z","snapshot_observed_at":"2026-08-07T18:08:22.261038Z","submitted_at":"2025-06-29T04:21:05Z","title":"Linear Complementary Pairs of Algebraic Geometry Codes via Kummer Extensions","version":1},"cited_work":{"arxiv_id":"2506.23081","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.23081","snapshot_observed_at":"2026-07-03T13:08:09.043559Z","title":"Linear complementary pairs of algebraic geometry codes via Kummer extensions","venue":null,"work_id":"abbd61dd-5ec3-4169-ad1e-8919db61a6e3","year":2025},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"cited_paper":"/paper/2506.23081","citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:faf0de9f87bb6201c511cfec247ba00ed4138f98f13a9e91707ec2c61f1448ed","observation_id":"f90d2d98-e180-4ff0-95f7-8c541bbb47f3","resolution":{"observed_at":"2026-07-03T13:08:09.045054Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2604.27146","last_updated":"2026-04-29T19:55:54Z","snapshot_observed_at":"2026-07-06T23:12:38.453388Z","submitted_at":"2026-04-29T19:55:54Z","title":"Characterization of non-special divisors of small degree on Kummer extensions and LCP codes","version":1},"cited_work":{"arxiv_id":"2604.27146","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.27146","snapshot_observed_at":"2026-07-03T13:08:09.037182Z","title":"Characterization of non-special divisors of small degree on Kummer extensions and LCP codes","venue":"math.AG","work_id":"33a5dc60-5a5e-47c1-af3d-b9c4f0df7b1c","year":2026},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"cited_paper":"/paper/2604.27146","citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:6eda9c68205378f8e23edb71d2103a6b9bd4fdce8d6de5265683c528e3314155","observation_id":"ae3cc663-a00e-41ec-8051-81c8896e9a2b","resolution":{"observed_at":"2026-07-03T13:08:09.038821Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2605.14046","last_updated":"2026-05-13T19:08:10Z","snapshot_observed_at":"2026-07-06T23:25:29.856145Z","submitted_at":"2026-05-13T19:08:10Z","title":"Construction of Non-special Divisors on Kummer Covers With Arbritary Ramification For LCP Codes","version":1},"cited_work":{"arxiv_id":"2605.14046","doi":null,"metadata_source":"pith","pith_arxiv_id":"2605.14046","snapshot_observed_at":"2026-07-03T13:08:09.034311Z","title":"Construction of Non-special Divisors on Kummer Covers With Arbritary Ramification For LCP Codes","venue":"math.AG","work_id":"0e7f230c-cbd0-4d3e-9711-9484d3f1d164","year":2026},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"cited_paper":"/paper/2605.14046","citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:aaba5e3f0911766c4734622e1ce55a6637b1d0eded92219f6b93f5db1420dd70","observation_id":"2db7fe8f-abc1-4f5a-b480-14836f71d631","resolution":{"observed_at":"2026-07-03T13:08:09.035758Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Code Construction on Fiber Products of Kummer Covers,","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:5c2fe4eca95e9aa9434743a2883b0f7a764278cc14f162e4759d4170d6ec8cfd","observation_id":"0dc5df70-5258-44be-822c-71c4328c5e96","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":null,"venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:52856c191a6bfb741543a26a89f3e89abba65434ec27734a3f84eefa1cb94b7e","observation_id":"948943c5-bea5-492a-b679-db0dec6cb98b","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"On the existence of non-special divisors of degree g and g - 1 in algebraic function fields overF q,","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:a686ab8977534f71439555038996b802981724281ea3af58794081f84d650245","observation_id":"5691f6b6-a4da-43d9-bfbf-86abe370cfef","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Pure gaps at many places and multi-point AG codes from arbitrary Kummer extensions,","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:2cdf50244fc1eff14daef39cde99fbdbc06f17cd226b1f32652e703def958ab7","observation_id":"f713e39d-9c1a-4667-8542-c6a5160466e4","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"On the index of the Weierstrass semigroup of a pair of points on a curve,","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:4b0ace7a0deaeaa7a03596df89ca93fd99c4dc27bfe6009c209030ae562851d3","observation_id":"2d8d719c-78bc-4426-a1f7-0b683d56d778","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"The Weierstrass Semigroup of an m-tuple of Collinear Points on a Hermitian Curve,","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:939a13b9c90d78dce18e20983e08ebf7324f6072c2039a78a4a590a74e931072","observation_id":"1617f901-3556-4e3b-80e2-4dc7a1b00203","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"On Goppa Codes and Weierstrass Gaps at Several Points,","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:4781cd6b6356ca67d706805612b5facd477ae42ce7a0facfe823b06fd08415ec","observation_id":"7b181326-ca35-404e-b703-1a4b9478333b","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"One- and Two-Point Codes Over Kummer Extensions,","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:b9c3f026ae09f250fbce98847582a8cefe71623167056ae4db8f3c91ad37c224","observation_id":"fdc252d5-435b-43eb-9134-5ba00a094fab","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Complete set of pure gaps in function fields,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:a399f91e585df8c7ecf7a1a156851acce712de374d40c4b800d543ac4229fb2f","observation_id":"194e6d60-e011-4958-b081-b4ac40dec52c","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"On generalized Weierstrass semigroups in arbitrary Kummer extensions ofF q(x),","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:ae3ea2f57ae51942357cd2dec631422da448914d74dbb9304da639d3305c736f","observation_id":"a3e91faa-34e2-46ea-b657-b514d10b467b","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Stichtenoth,Algebraic Function Fields and Codes","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:1ecb00df5008c751be50e17705114899d3a2026e80d109cc1e690407475a5622","observation_id":"29d3e71f-d78d-49bf-b029-08f2baea60f0","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2605.14583","last_updated":"2026-05-14T08:54:10Z","snapshot_observed_at":"2026-07-06T23:25:58.895612Z","submitted_at":"2026-05-14T08:54:10Z","title":"Weierstrass semigroups at totally ramified places of degree one on Kummer extensions","version":1},"cited_work":{"arxiv_id":"2605.14583","doi":null,"metadata_source":"pith","pith_arxiv_id":"2605.14583","snapshot_observed_at":"2026-07-03T13:08:09.040043Z","title":"Weierstrass semigroups at totally ramified places of degree one on Kummer extensions","venue":"math.AG","work_id":"f13bbc7c-6a72-465a-a928-ecabedf434db","year":2026},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"cited_paper":"/paper/2605.14583","citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:54829212aebcf70abc4edc4fc1f535a3651030ffa8b318989dbed3eed4a0d2e4","observation_id":"b9c7f7f2-7298-42b4-b243-7abff4c3f78a","resolution":{"observed_at":"2026-07-03T13:08:09.042291Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"Multi-point codes over Kummer extensions,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:04003651511352d30e94a0bd5706f6950cac2a93d4658c0b048dbe45dc0499b2","observation_id":"4c59b6e4-621d-49ff-a9ec-e112e6dfa4a0","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T08:23:45.294590Z","title":"A new family of maximal curves over a finite field,","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-06-27T08:23:45.294590Z"},"links":{"citing_paper":"/paper/2606.11764"},"observation_digest":"sha256:6a5b49b2819525e91ec4149f5d80b371fa546aedb991aa29c04d7d986d5d25ed","observation_id":"6ef79163-30ab-4ae3-8cc3-2e7a0d2c8ff5","resolution":{"observed_at":"2026-06-27T08:23:45.294590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.11764","last_updated":"2026-06-10T07:43:09Z","latest_version":1,"primary_category":"cs.IT","snapshot_observed_at":"2026-08-06T11:38:15.222370Z","submitted_at":"2026-06-10T07:43:09Z","title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions"},"reference_resolution":{"displayed":42,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":38,"verified_exact":4,"verified_fuzzy":0},"total_outbound_references":42},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 0 inbound Pith citation observations for arXiv:2606.11764."}