{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:O262VLSKSZYHRBW42HCHLHPYFK","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":"b4b9970de7f7722ba4fc221806858f07eaca9e2ed6f1d155e5d86d7469d965af","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-11T04:57:10Z","title_canon_sha256":"24660646a4cde76c81418de7e5d5c232db8c661eeb502ba94628e909be2aa1c5"},"schema_version":"1.0","source":{"id":"1601.02320","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02320","created_at":"2026-05-18T00:40:51Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02320v2","created_at":"2026-05-18T00:40:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02320","created_at":"2026-05-18T00:40:51Z"},{"alias_kind":"pith_short_12","alias_value":"O262VLSKSZYH","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O262VLSKSZYHRBW4","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O262VLSK","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:7fc0a8f1718c0ebe2ecbd2844a658714d903d15c28313c54d3c907f378c19d12","target":"graph","created_at":"2026-05-18T00:40:51Z","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":"Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. In this paper, for an odd prime $p$, we propose a class of $p$-ary linear codes by choosing a proper defining set. Their weight enumerators and complete weight enumerators are presented explicitly. The results show that they are linear codes with three weights and suitable for the constructions of authentication codes and secret sharing schemes.","authors_text":"Chang-An Zhao, Shudi Yang, Zheng-an Yao","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-11T04:57:10Z","title":"A Class of Three-Weight Linear Codes and Their Complete Weight Enumerators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02320","kind":"arxiv","version":2},"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":"sha256:479034a8ce7c80870ff5473922ac3a555ff170c8c39aa4135a855a29aa7c6f12","target":"record","created_at":"2026-05-18T00:40:51Z","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":"b4b9970de7f7722ba4fc221806858f07eaca9e2ed6f1d155e5d86d7469d965af","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-11T04:57:10Z","title_canon_sha256":"24660646a4cde76c81418de7e5d5c232db8c661eeb502ba94628e909be2aa1c5"},"schema_version":"1.0","source":{"id":"1601.02320","kind":"arxiv","version":2}},"canonical_sha256":"76bdaaae4a96707886dcd1c4759df82a9d095bdfffa7e3c475cff27ab6102c7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76bdaaae4a96707886dcd1c4759df82a9d095bdfffa7e3c475cff27ab6102c7b","first_computed_at":"2026-05-18T00:40:51.812920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:51.812920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Fg09SacXAuP5I4kAf8ahdqsRd/AljksNrebz/sui/8DsS4FxvJYC7kDkn1t5fR/gUa7YJm9DvdpuS5hhQhJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:51.813653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02320","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:479034a8ce7c80870ff5473922ac3a555ff170c8c39aa4135a855a29aa7c6f12","sha256:7fc0a8f1718c0ebe2ecbd2844a658714d903d15c28313c54d3c907f378c19d12"],"state_sha256":"5e09944cec83ca41d6c2ab95e89e9404964bad0a398805a663227e40827afae7"}