{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CR4STMCGZMJTAKIYH4ZA3G6GLO","short_pith_number":"pith:CR4STMCG","schema_version":"1.0","canonical_sha256":"147929b046cb133029183f320d9bc65b96b39ac12d703e2948fe4ebb5e6a931e","source":{"kind":"arxiv","id":"1612.00914","version":1},"attestation_state":"computed","paper":{"title":"Some ternary cubic two-weight codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Daitao Huang, Minjia Shi, Patrick Sole","submitted_at":"2016-12-03T02:13:51Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.00914","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-03T02:13:51Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d8c3fc31fc2447a61b874411f90b52bcc57dfc3df28616d2494a80fefb32bd21","abstract_canon_sha256":"05f96c4b2b6d481b3645950399c01b457e8158b9a75f5db7851891b63dca01a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:53.833222Z","signature_b64":"cMUt7Tvs1Kx8xGUQHeLx6ydjWXhj/ZURiG0++bBNq7pinckkIpqo4AtFE38VOU4YhXvgZh6iqb6peoiYbiOJBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"147929b046cb133029183f320d9bc65b96b39ac12d703e2948fe4ebb5e6a931e","last_reissued_at":"2026-05-18T00:55:53.832811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:53.832811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some ternary cubic two-weight codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Daitao Huang, Minjia Shi, Patrick Sole","submitted_at":"2016-12-03T02:13:51Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00914","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.00914","created_at":"2026-05-18T00:55:53.832879+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.00914v1","created_at":"2026-05-18T00:55:53.832879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00914","created_at":"2026-05-18T00:55:53.832879+00:00"},{"alias_kind":"pith_short_12","alias_value":"CR4STMCGZMJT","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CR4STMCGZMJTAKIY","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CR4STMCG","created_at":"2026-05-18T12:30:09.641336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CR4STMCGZMJTAKIYH4ZA3G6GLO","json":"https://pith.science/pith/CR4STMCGZMJTAKIYH4ZA3G6GLO.json","graph_json":"https://pith.science/api/pith-number/CR4STMCGZMJTAKIYH4ZA3G6GLO/graph.json","events_json":"https://pith.science/api/pith-number/CR4STMCGZMJTAKIYH4ZA3G6GLO/events.json","paper":"https://pith.science/paper/CR4STMCG"},"agent_actions":{"view_html":"https://pith.science/pith/CR4STMCGZMJTAKIYH4ZA3G6GLO","download_json":"https://pith.science/pith/CR4STMCGZMJTAKIYH4ZA3G6GLO.json","view_paper":"https://pith.science/paper/CR4STMCG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.00914&json=true","fetch_graph":"https://pith.science/api/pith-number/CR4STMCGZMJTAKIYH4ZA3G6GLO/graph.json","fetch_events":"https://pith.science/api/pith-number/CR4STMCGZMJTAKIYH4ZA3G6GLO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CR4STMCGZMJTAKIYH4ZA3G6GLO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CR4STMCGZMJTAKIYH4ZA3G6GLO/action/storage_attestation","attest_author":"https://pith.science/pith/CR4STMCGZMJTAKIYH4ZA3G6GLO/action/author_attestation","sign_citation":"https://pith.science/pith/CR4STMCGZMJTAKIYH4ZA3G6GLO/action/citation_signature","submit_replication":"https://pith.science/pith/CR4STMCGZMJTAKIYH4ZA3G6GLO/action/replication_record"}},"created_at":"2026-05-18T00:55:53.832879+00:00","updated_at":"2026-05-18T00:55:53.832879+00:00"}