{"paper":{"title":"Generator polynomials and generator matrix for quasi cyclic codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Zahra Sepasdar","submitted_at":"2017-04-28T05:56:01Z","abstract_excerpt":"Quasi-cyclic (QC) codes form an important generalization of cyclic codes. It is well know that QC codes of length $s\\ell$ with index $s$ over the finite field $\\mathbb{F}$ are $\\mathbb{F}[y]$-submodules of the ring $\\frac{\\mathbb{F}[x,y]}{< x^s-1,y^{\\ell}-1 >}$. The aim of the present paper, is to study QC codes of length $s\\ell$ with index $s$ over the finite field $\\mathbb{F}$ and find generator polynomials and generator matrix for these codes. To achieve this aim, we apply a novel method to find generator polynomials for $\\mathbb{F}[y]$-submodules of $\\frac{\\mathbb{F}[x,y]}{< x^s-1,y^{\\ell}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08815","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"}