{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:F4OQ6CNHOLOGCBVPK4I72AJ57E","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":"4fdceea141a3517de7218e3c6ccd2e773003c06a87f6679c8d747a0bfab86248","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2008-02-13T12:59:04Z","title_canon_sha256":"8588602c4c2017c060ec4700cebc68fe21e5e05f3b6a08d20dca90cd39763607"},"schema_version":"1.0","source":{"id":"0802.1815","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.1815","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"0802.1815v1","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.1815","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"F4OQ6CNHOLOG","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"F4OQ6CNHOLOGCBVP","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"F4OQ6CNH","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:ec10c5418743d07551b5632be78c14f3da9460dbb26d493932a2cc468dd5590a","target":"graph","created_at":"2026-05-18T00:59:11Z","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":"By employing the residue polynomials, a construction of constant-composition codes is given. This construction generalizes the one proposed by Xing[16]. It turns out that when d=3 this construction gives a lower bound of constant-composition codes improving the one in [10]. Moreover, for d>3, we give a lower bound on maximal size of constant-composition codes. In particular, our bound for d=5 gives the best possible size of constant-composition codes up to magnitude.","authors_text":"Yang Ding","cross_cats":["math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2008-02-13T12:59:04Z","title":"A Construction for Constant-Composition Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.1815","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":"sha256:34ceeaed395e9efe4d381b6e42eaee7c9479e9b452835969a072f96d7f3bc4b0","target":"record","created_at":"2026-05-18T00:59:11Z","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":"4fdceea141a3517de7218e3c6ccd2e773003c06a87f6679c8d747a0bfab86248","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2008-02-13T12:59:04Z","title_canon_sha256":"8588602c4c2017c060ec4700cebc68fe21e5e05f3b6a08d20dca90cd39763607"},"schema_version":"1.0","source":{"id":"0802.1815","kind":"arxiv","version":1}},"canonical_sha256":"2f1d0f09a772dc6106af5711fd013df9316710b593eb989c6bfc54b7ba63aab4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f1d0f09a772dc6106af5711fd013df9316710b593eb989c6bfc54b7ba63aab4","first_computed_at":"2026-05-18T00:59:11.902695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:11.902695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XwPVVROaIzVAtcTr+EcgWuhiiLrdRPIccaw8Vkeg0gZ8wLOOg7QD/OFT5RyW+3wN8ZE5daXhO7447i5IYbF3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:11.903441Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.1815","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34ceeaed395e9efe4d381b6e42eaee7c9479e9b452835969a072f96d7f3bc4b0","sha256:ec10c5418743d07551b5632be78c14f3da9460dbb26d493932a2cc468dd5590a"],"state_sha256":"f1e936468cb5cab1eadc0a8bd8d11e89d00b91435ebdb8354b9821ba874afe9a"}