{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:5CIKE6LXQBUPMCVGYY5OXGTLKC","short_pith_number":"pith:5CIKE6LX","canonical_record":{"source":{"id":"2303.16729","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.IT","submitted_at":"2023-03-29T14:34:27Z","cross_cats_sorted":["cs.CR","math.IT"],"title_canon_sha256":"6532df5a0465892941b02b828e0e7300fa9e63684f78ccf1213b21a86e7d9b29","abstract_canon_sha256":"5d5967e3a12c1e3771fe4c7de9587c37c149a056108a606083b375d461ff66b4"},"schema_version":"1.0"},"canonical_sha256":"e890a279778068f60aa6c63aeb9a6b5083689c2e6001809fa0bd3df3d52dc5f4","source":{"kind":"arxiv","id":"2303.16729","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.16729","created_at":"2026-07-05T05:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"2303.16729v1","created_at":"2026-07-05T05:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.16729","created_at":"2026-07-05T05:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"5CIKE6LXQBUP","created_at":"2026-07-05T05:56:09Z"},{"alias_kind":"pith_short_16","alias_value":"5CIKE6LXQBUPMCVG","created_at":"2026-07-05T05:56:09Z"},{"alias_kind":"pith_short_8","alias_value":"5CIKE6LX","created_at":"2026-07-05T05:56:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:5CIKE6LXQBUPMCVGYY5OXGTLKC","target":"record","payload":{"canonical_record":{"source":{"id":"2303.16729","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.IT","submitted_at":"2023-03-29T14:34:27Z","cross_cats_sorted":["cs.CR","math.IT"],"title_canon_sha256":"6532df5a0465892941b02b828e0e7300fa9e63684f78ccf1213b21a86e7d9b29","abstract_canon_sha256":"5d5967e3a12c1e3771fe4c7de9587c37c149a056108a606083b375d461ff66b4"},"schema_version":"1.0"},"canonical_sha256":"e890a279778068f60aa6c63aeb9a6b5083689c2e6001809fa0bd3df3d52dc5f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:56:09.744760Z","signature_b64":"ptuBbH5hIWV1au3tfO9MXE6S4AD3GuCIuN6Vl8wqJzGUWzTD8bUEfT1JqCSRJdNPvf+edyeoPX0bh2SqU1ybAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e890a279778068f60aa6c63aeb9a6b5083689c2e6001809fa0bd3df3d52dc5f4","last_reissued_at":"2026-07-05T05:56:09.744336Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:56:09.744336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.16729","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PzgE494mny9dJsLKHTSuPrqZFj+wOTCWzhA+ctSwIrRYwO6z12aubG7mQcd3rqciW0TxGCxxE7y2dPBDbQoZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:05:32.518054Z"},"content_sha256":"47899d304dcff2dd6c36e530b9df2b7028706638dd8d03ec94ecaee17bf7318d","schema_version":"1.0","event_id":"sha256:47899d304dcff2dd6c36e530b9df2b7028706638dd8d03ec94ecaee17bf7318d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:5CIKE6LXQBUPMCVGYY5OXGTLKC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.CR","math.IT"],"primary_cat":"cs.IT","authors_text":"Jon-Lark Kim, Minjia Shi, Shitao Li, Tor Helleseth","submitted_at":"2023-03-29T14:34:27Z","abstract_excerpt":"The purpose of this paper is two-fold. First, we characterize the existence of binary self-orthogonal codes meeting the Griesmer bound by employing Solomon-Stiffler codes and some related residual codes. Second, using such a characterization, we determine the exact value of $d_{so}(n,7)$ except for five special cases and the exact value of $d_{so}(n,8)$ except for 41 special cases, where $d_{so}(n,k)$ denotes the largest minimum distance among all binary self-orthogonal $[n, k]$ codes. Currently, the exact value of $d_{so}(n,k)$ $(k \\le 6)$ was determined by Shi et al. (2022). In addition, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.16729","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.16729/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yYualp0keOTdv+lW4EW99/rxq3nNof0/vfCPX8clMRZ9VARarFTsU6w6A8Z3wDlMf6+JlePSF6rFuh6zn6FgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:05:32.518451Z"},"content_sha256":"f58779e5f9928bdd07b2fb78ccb10a3101b43d183d9b0caec28a4e5c25c3ea9a","schema_version":"1.0","event_id":"sha256:f58779e5f9928bdd07b2fb78ccb10a3101b43d183d9b0caec28a4e5c25c3ea9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5CIKE6LXQBUPMCVGYY5OXGTLKC/bundle.json","state_url":"https://pith.science/pith/5CIKE6LXQBUPMCVGYY5OXGTLKC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5CIKE6LXQBUPMCVGYY5OXGTLKC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-06T19:05:32Z","links":{"resolver":"https://pith.science/pith/5CIKE6LXQBUPMCVGYY5OXGTLKC","bundle":"https://pith.science/pith/5CIKE6LXQBUPMCVGYY5OXGTLKC/bundle.json","state":"https://pith.science/pith/5CIKE6LXQBUPMCVGYY5OXGTLKC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5CIKE6LXQBUPMCVGYY5OXGTLKC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5CIKE6LXQBUPMCVGYY5OXGTLKC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5d5967e3a12c1e3771fe4c7de9587c37c149a056108a606083b375d461ff66b4","cross_cats_sorted":["cs.CR","math.IT"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.IT","submitted_at":"2023-03-29T14:34:27Z","title_canon_sha256":"6532df5a0465892941b02b828e0e7300fa9e63684f78ccf1213b21a86e7d9b29"},"schema_version":"1.0","source":{"id":"2303.16729","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.16729","created_at":"2026-07-05T05:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"2303.16729v1","created_at":"2026-07-05T05:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.16729","created_at":"2026-07-05T05:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"5CIKE6LXQBUP","created_at":"2026-07-05T05:56:09Z"},{"alias_kind":"pith_short_16","alias_value":"5CIKE6LXQBUPMCVG","created_at":"2026-07-05T05:56:09Z"},{"alias_kind":"pith_short_8","alias_value":"5CIKE6LX","created_at":"2026-07-05T05:56:09Z"}],"graph_snapshots":[{"event_id":"sha256:f58779e5f9928bdd07b2fb78ccb10a3101b43d183d9b0caec28a4e5c25c3ea9a","target":"graph","created_at":"2026-07-05T05:56:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2303.16729/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of this paper is two-fold. First, we characterize the existence of binary self-orthogonal codes meeting the Griesmer bound by employing Solomon-Stiffler codes and some related residual codes. Second, using such a characterization, we determine the exact value of $d_{so}(n,7)$ except for five special cases and the exact value of $d_{so}(n,8)$ except for 41 special cases, where $d_{so}(n,k)$ denotes the largest minimum distance among all binary self-orthogonal $[n, k]$ codes. Currently, the exact value of $d_{so}(n,k)$ $(k \\le 6)$ was determined by Shi et al. (2022). In addition, we ","authors_text":"Jon-Lark Kim, Minjia Shi, Shitao Li, Tor Helleseth","cross_cats":["cs.CR","math.IT"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.IT","submitted_at":"2023-03-29T14:34:27Z","title":"Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.16729","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:47899d304dcff2dd6c36e530b9df2b7028706638dd8d03ec94ecaee17bf7318d","target":"record","created_at":"2026-07-05T05:56:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5d5967e3a12c1e3771fe4c7de9587c37c149a056108a606083b375d461ff66b4","cross_cats_sorted":["cs.CR","math.IT"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.IT","submitted_at":"2023-03-29T14:34:27Z","title_canon_sha256":"6532df5a0465892941b02b828e0e7300fa9e63684f78ccf1213b21a86e7d9b29"},"schema_version":"1.0","source":{"id":"2303.16729","kind":"arxiv","version":1}},"canonical_sha256":"e890a279778068f60aa6c63aeb9a6b5083689c2e6001809fa0bd3df3d52dc5f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e890a279778068f60aa6c63aeb9a6b5083689c2e6001809fa0bd3df3d52dc5f4","first_computed_at":"2026-07-05T05:56:09.744336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:56:09.744336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ptuBbH5hIWV1au3tfO9MXE6S4AD3GuCIuN6Vl8wqJzGUWzTD8bUEfT1JqCSRJdNPvf+edyeoPX0bh2SqU1ybAg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:56:09.744760Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.16729","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47899d304dcff2dd6c36e530b9df2b7028706638dd8d03ec94ecaee17bf7318d","sha256:f58779e5f9928bdd07b2fb78ccb10a3101b43d183d9b0caec28a4e5c25c3ea9a"],"state_sha256":"9130a1f2d0859cdc2b17b16bd6d660592f9a7f6ee727f9baf06315631fb1b7e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QxR+mdirN0QYJgeWGz4iibkKSAqu4nliAzh6veN9euS7ePo3GXDD0NVwsvdPb3LZRa6rZIln1WbnWuKlVJhPAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T19:05:32.520384Z","bundle_sha256":"c7110604086d3a5f272028b8bdf2357680c1c68587605ccb1f7309d7a374821f"}}