{"paper":{"title":"A class of $p$-ary cyclic codes and their weight enumerators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hongwei Liu, Long Yu","submitted_at":"2014-07-08T10:59:01Z","abstract_excerpt":"Let $m$, $k$ be positive integers such that $\\frac{m}{\\gcd(m,k)}\\geq 3$, $p$ be an odd prime and $\\pi $ be a primitive element of $\\mathbb{F}_{p^m}$. Let $h_1(x)$ and $h_2(x)$ be the minimal polynomials of $-\\pi^{-1}$ and $\\pi^{-\\frac{p^k+1}{2}}$ over $\\mathbb{F}_p$, respectively. In the case of odd $\\frac{m}{\\gcd(m,k)}$, when $k$ is even, $\\gcd(m,k)$ is odd or when $\\frac{k}{\\gcd(m,k)}$ is odd, Zhou et~al. in \\cite{zhou} obtained the weight distribution of a class of cyclic codes $\\mathcal{C}$ over $\\mathbb{F}_p$ with parity-check polynomial $h_1(x)h_2(x)$. In this paper, we further investiga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2032","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"}