{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:EMD6K53GA5MOVVLWRBQ3YW5KZF","short_pith_number":"pith:EMD6K53G","schema_version":"1.0","canonical_sha256":"2307e577660758ead5768861bc5baac97e49de547ef12427ea22c7f54eaede9d","source":{"kind":"arxiv","id":"2605.14848","version":1},"attestation_state":"computed","paper":{"title":"Construction of Minimal Ternary Linear Codes with Dimension $n+2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Haibo Liu, Qunying Liao, Xin Guo","submitted_at":"2026-05-14T13:56:15Z","abstract_excerpt":"Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, secure two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then determining their weight distributions have been interesting in coding theory and cryptography. In this paper, a generic construction for ternary linear codes with dimension $m+2$ is presented, where $m$ is an integer, and a necessary and sufficient condition for this ternary linear code to be minimal is derived. Based on this condition and exponential sums, a"},"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":"2605.14848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-05-14T13:56:15Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"f26e890257a5eb861700dfced44a54ff1e474ff9c1482fa22b154fa4131e7c2f","abstract_canon_sha256":"fb663a19043cf96cac2ac1bc0088f195a1030f2727c327d7faf035266531a40b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:38:56.352270Z","signature_b64":"79GPP6Qn+xa81Wlr20C6E6a1CojkTTO/JxGbzvoezkf4If9YmtYqkBGr5vIrdtpVM5sdXEbWOalkiXoysoQrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2307e577660758ead5768861bc5baac97e49de547ef12427ea22c7f54eaede9d","last_reissued_at":"2026-05-17T23:38:56.351552Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:38:56.351552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Construction of Minimal Ternary Linear Codes with Dimension $n+2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Haibo Liu, Qunying Liao, Xin Guo","submitted_at":"2026-05-14T13:56:15Z","abstract_excerpt":"Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, secure two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then determining their weight distributions have been interesting in coding theory and cryptography. In this paper, a generic construction for ternary linear codes with dimension $m+2$ is presented, where $m$ is an integer, and a necessary and sufficient condition for this ternary linear code to be minimal is derived. Based on this condition and exponential sums, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.14848","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":"2605.14848","created_at":"2026-05-17T23:38:56.351664+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.14848v1","created_at":"2026-05-17T23:38:56.351664+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14848","created_at":"2026-05-17T23:38:56.351664+00:00"},{"alias_kind":"pith_short_12","alias_value":"EMD6K53GA5MO","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"EMD6K53GA5MOVVLW","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"EMD6K53G","created_at":"2026-05-18T12:33:37.589309+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/EMD6K53GA5MOVVLWRBQ3YW5KZF","json":"https://pith.science/pith/EMD6K53GA5MOVVLWRBQ3YW5KZF.json","graph_json":"https://pith.science/api/pith-number/EMD6K53GA5MOVVLWRBQ3YW5KZF/graph.json","events_json":"https://pith.science/api/pith-number/EMD6K53GA5MOVVLWRBQ3YW5KZF/events.json","paper":"https://pith.science/paper/EMD6K53G"},"agent_actions":{"view_html":"https://pith.science/pith/EMD6K53GA5MOVVLWRBQ3YW5KZF","download_json":"https://pith.science/pith/EMD6K53GA5MOVVLWRBQ3YW5KZF.json","view_paper":"https://pith.science/paper/EMD6K53G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.14848&json=true","fetch_graph":"https://pith.science/api/pith-number/EMD6K53GA5MOVVLWRBQ3YW5KZF/graph.json","fetch_events":"https://pith.science/api/pith-number/EMD6K53GA5MOVVLWRBQ3YW5KZF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EMD6K53GA5MOVVLWRBQ3YW5KZF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EMD6K53GA5MOVVLWRBQ3YW5KZF/action/storage_attestation","attest_author":"https://pith.science/pith/EMD6K53GA5MOVVLWRBQ3YW5KZF/action/author_attestation","sign_citation":"https://pith.science/pith/EMD6K53GA5MOVVLWRBQ3YW5KZF/action/citation_signature","submit_replication":"https://pith.science/pith/EMD6K53GA5MOVVLWRBQ3YW5KZF/action/replication_record"}},"created_at":"2026-05-17T23:38:56.351664+00:00","updated_at":"2026-05-17T23:38:56.351664+00:00"}