{"paper":{"title":"(Sigma-Delta) Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"A. Leroy, M. Boulagouaz","submitted_at":"2013-04-24T09:11:36Z","abstract_excerpt":"In this paper we introduce the notion of cyclic ($f(t),\\sigma,\\delta$)-codes for $f(t)\\in \\Ore$. These codes generalize the $\\theta$-codes as introduced by D. Boucher, F. Ulmer, W. Geiselmann \\cite{BGU}. We construct generic and control matrices for these codes. As a particular case the ($\\si,\\de$)-$W$-code associated to a Wedderburn polynomial are defined and we show that their control matrices are given by generalized Vandermonde matrices. All the Wedderburn polynomials of $\\mathbb F_q[t;\\theta]$ are described and their control matrices are presented. A key role will be played by the pseudo-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6518","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":""},"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"}