{"paper":{"title":"Construction of quasi-cyclic self-dual codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Heisook Lee, Jon-Lark Kim, Sunghyu Han, Yoonjin Lee","submitted_at":"2012-01-29T04:12:48Z","abstract_excerpt":"There is a one-to-one correspondence between $\\ell$-quasi-cyclic codes over a finite field $\\mathbb F_q$ and linear codes over a ring $R = \\mathbb F_q[Y]/(Y^m-1)$. Using this correspondence, we prove that every $\\ell$-quasi-cyclic self-dual code of length $m\\ell$ over a finite field $\\mathbb F_q$ can be obtained by the {\\it building-up} construction, provided that char $(\\mathbb F_q)=2$ or $q \\equiv 1 \\pmod 4$, $m$ is a prime $p$, and $q$ is a primitive element of $\\mathbb F_p$. We determine possible weight enumerators of a binary $\\ell$-quasi-cyclic self-dual code of length $p\\ell$ (with $p$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6012","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"}