{"paper":{"title":"A Study Of Skew-Polycyclic Codes Over A Non-Chain Ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.RA"],"primary_cat":"cs.IT","authors_text":"Manju Khan, Seema Antil, Seema Chahal, Sugandha Maheshwary","submitted_at":"2026-07-09T09:46:32Z","abstract_excerpt":"For a prime \\(p\\) and a positive integer \\(m\\), let \\(\\mathbb{F}_{p^m}\\) be the finite field of cardinality \\(p^m\\), and let\n  $\n  R_{u^2,v^2,p^m}\n  =\\mathbb{F}_{p^m}+u\\mathbb{F}_{p^m}+v\\mathbb{F}_{p^m}\n  +uv\\mathbb{F}_{p^m},\n  ~ u^2=v^2=0,\\ uv=vu,\n  $\n  be a finite non-chain ring. In this paper, we study skew polycyclic codes of length \\(lj\\) associated with \\(f(x)^j\\), where \\(f(x)\\) is a central polynomial of degree \\(l\\) in $R_{u^2, v^2, p^m}[x; \\Theta],$ where $\\Theta$ being an automorphism of \\(R_{u^2,v^2,p^m}\\). We describe these codes, characterize free skew polycyclic codes, and deter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08304","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.08304/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}