{"paper":{"title":"Twisted Centralizer Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.AC","math.IT"],"primary_cat":"math.CO","authors_text":"Adel Alahmadi, Bahattin Yildiz, Cheryl E. Praeger, Patrick Sol\\'e, S. P. Glasby","submitted_at":"2016-08-14T09:26:14Z","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 $n^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04079","kind":"arxiv","version":3},"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"}