{"paper":{"title":"Linear and cyclic codes over some special rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Linear and cyclic codes are defined over the ring Z2[u,v] modulo u squared times (1 plus u) and v squared times (1 plus v squared).","cross_cats":["math.IT","math.RA"],"primary_cat":"cs.IT","authors_text":"Bianca Liana Bercea-Straton, Cristina Flaut","submitted_at":"2026-05-04T18:02:03Z","abstract_excerpt":"In this paper, we describe linear and cyclic codes over the rings of the form $R_{s,p}=\\mathbb{Z}_{p}[u]/\\left( f\\left(u\\right) /\\left( u-s\\right) \\right)$, where $p$ is a prime number and $f\\left( u\\right) =u^{p}-u$, with $s\\in \\{0,1,...,p-1\\}$."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In this paper, we describe linear and cyclic codes over the ring Z2[u,v](u2(1+u),v2(1+v2)).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The given ring admits the standard definitions of linear and cyclic codes without additional compatibility conditions that would invalidate the usual generator-matrix or ideal-based constructions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Linear and cyclic codes are described over the ring Z₂[u,v]/(u²(1+u), v²(1+v²)).","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Linear and cyclic codes are defined over the ring Z2[u,v] modulo u squared times (1 plus u) and v squared times (1 plus v squared).","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a483a694aef3d1d1c8aa0a2b0e28fcc055c6b3f2d377ec701818eebfee0184ac"},"source":{"id":"2605.03031","kind":"arxiv","version":2},"verdict":{"id":"1d84e1bb-8dc8-48a3-8b9b-408a280ed29e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T17:29:13.545970Z","strongest_claim":"In this paper, we describe linear and cyclic codes over the ring Z2[u,v](u2(1+u),v2(1+v2)).","one_line_summary":"Linear and cyclic codes are described over the ring Z₂[u,v]/(u²(1+u), v²(1+v²)).","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The given ring admits the standard definitions of linear and cyclic codes without additional compatibility conditions that would invalidate the usual generator-matrix or ideal-based constructions.","pith_extraction_headline":"Linear and cyclic codes are defined over the ring Z2[u,v] modulo u squared times (1 plus u) and v squared times (1 plus v squared)."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.03031/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T14:39:25.952204Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T02:01:22.196430Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:47:20.966932Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f860dac6e9f3e9ab37bea124182844b8ee3dbc36530033daa7a55cd68c83f5e2"},"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"}