{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CR4STMCGZMJTAKIYH4ZA3G6GLO","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":"05f96c4b2b6d481b3645950399c01b457e8158b9a75f5db7851891b63dca01a4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-03T02:13:51Z","title_canon_sha256":"d8c3fc31fc2447a61b874411f90b52bcc57dfc3df28616d2494a80fefb32bd21"},"schema_version":"1.0","source":{"id":"1612.00914","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00914","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00914v1","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00914","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"pith_short_12","alias_value":"CR4STMCGZMJT","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CR4STMCGZMJTAKIY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CR4STMCG","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:0ecfbb25f6b3fc68ef66466f4065553b2ff35920ffd18d94e87e55035edf296d","target":"graph","created_at":"2026-05-18T00:55:53Z","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"},"paper":{"abstract_excerpt":"We study trace codes with defining set $L,$ a subgroup of the multiplicative group of an extension of degree $m$ of the alphabet ring $\\mathbb{F}_3+u\\mathbb{F}_3+u^{2}\\mathbb{F}_{3},$ with $u^{3}=1.$ These codes are abelian, and their ternary images are quasi-cyclic of co-index three (a.k.a. cubic codes). Their Lee weight distributions are computed by using Gauss sums. These codes have three nonzero weights when $m$ is singly-even and $|L|=\\frac{3^{3m}-3^{2m}}{2}.$ When $m$ is odd, and $|L|=\\frac{3^{3m}-3^{2m}}{2}$, or $|L|={3^{3m}-3^{2m}}$ and $m$ is a positive integer, we obtain two new infi","authors_text":"Daitao Huang, Minjia Shi, Patrick Sole","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-03T02:13:51Z","title":"Some ternary cubic two-weight codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00914","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:d8365244fc4c50d411d1082528844292e009aa44294b35b96697e7b859f5eb43","target":"record","created_at":"2026-05-18T00:55:53Z","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":"05f96c4b2b6d481b3645950399c01b457e8158b9a75f5db7851891b63dca01a4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-03T02:13:51Z","title_canon_sha256":"d8c3fc31fc2447a61b874411f90b52bcc57dfc3df28616d2494a80fefb32bd21"},"schema_version":"1.0","source":{"id":"1612.00914","kind":"arxiv","version":1}},"canonical_sha256":"147929b046cb133029183f320d9bc65b96b39ac12d703e2948fe4ebb5e6a931e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"147929b046cb133029183f320d9bc65b96b39ac12d703e2948fe4ebb5e6a931e","first_computed_at":"2026-05-18T00:55:53.832811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:53.832811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cMUt7Tvs1Kx8xGUQHeLx6ydjWXhj/ZURiG0++bBNq7pinckkIpqo4AtFE38VOU4YhXvgZh6iqb6peoiYbiOJBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:53.833222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.00914","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8365244fc4c50d411d1082528844292e009aa44294b35b96697e7b859f5eb43","sha256:0ecfbb25f6b3fc68ef66466f4065553b2ff35920ffd18d94e87e55035edf296d"],"state_sha256":"7a3c1a667b0866e9158da311e16ff973bea33cd063afb2855bdf0fa54ba61291"}