{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5VC5XMCZ4E7BJSEYLEWZIEEKNA","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":"8eb63bd3b17a112555a13e816da73093aff8946e67b0ebef3a136564f3b04173","cross_cats_sorted":["cs.IT","math.AC","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-14T09:26:14Z","title_canon_sha256":"e14ab4bea223decaaf8b445af5944df853995b4df5eadf5d4da21c50e1ccc9c6"},"schema_version":"1.0","source":{"id":"1608.04079","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04079","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04079v3","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04079","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"pith_short_12","alias_value":"5VC5XMCZ4E7B","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5VC5XMCZ4E7BJSEY","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5VC5XMCZ","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:6bb478219e3aa533ef6df4f1fd0e57105690069a92b9c430a547a56e1dd16c79","target":"graph","created_at":"2026-05-18T00:48:54Z","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":"Given an $n\\times n$ matrix $A$ over a field $F$ and a scalar $a\\in F$, we consider the linear codes $C(A,a):=\\{B\\in F^{n\\times n}\\mid \\,AB=aBA\\}$ of length $n^2$. We call $C(A,a)$ a twisted centralizer code. We investigate properties of these codes including their dimensions, minimum distances, parity-check matrices, syndromes, and automorphism groups. The minimal distance of a centralizer code (when $a=1$) is at most $n$, however for $a\\ne 0,1$ the minimal distance can be much larger, as large as $n^2$.","authors_text":"Adel Alahmadi, Bahattin Yildiz, Cheryl E. Praeger, Patrick Sol\\'e, S. P. Glasby","cross_cats":["cs.IT","math.AC","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-14T09:26:14Z","title":"Twisted Centralizer Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04079","kind":"arxiv","version":3},"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":"sha256:2992324f6c25ae12230780fa7ae0b99a1b0ce5c00903b0f086deb618ed7f7d28","target":"record","created_at":"2026-05-18T00:48:54Z","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":"8eb63bd3b17a112555a13e816da73093aff8946e67b0ebef3a136564f3b04173","cross_cats_sorted":["cs.IT","math.AC","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-14T09:26:14Z","title_canon_sha256":"e14ab4bea223decaaf8b445af5944df853995b4df5eadf5d4da21c50e1ccc9c6"},"schema_version":"1.0","source":{"id":"1608.04079","kind":"arxiv","version":3}},"canonical_sha256":"ed45dbb059e13e14c898592d94108a6815ce896677dbbb22c34d1d2f917d92e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed45dbb059e13e14c898592d94108a6815ce896677dbbb22c34d1d2f917d92e5","first_computed_at":"2026-05-18T00:48:54.298685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:54.298685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/VdGbzv7+q5ry7eEq663g091mkJB76UdxGlTdThwELt0psCe9icpuVAwd0pfxk8VKu7uv/0Uq3sN+XFuXjt1AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:54.299504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04079","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2992324f6c25ae12230780fa7ae0b99a1b0ce5c00903b0f086deb618ed7f7d28","sha256:6bb478219e3aa533ef6df4f1fd0e57105690069a92b9c430a547a56e1dd16c79"],"state_sha256":"61185f329057e584bf5bb52cc1b41dafeab56091ac41ca45ff5c5e555b769991"}