{"paper":{"title":"Weight distributions of cyclic codes with respect to pairwise coprime order elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chengju Li, Fengwei Li, Qin Yue","submitted_at":"2013-06-24T23:35:12Z","abstract_excerpt":"Let $\\Bbb F_r$ be an extension of a finite field $\\Bbb F_q$ with $r=q^m$. Let each $g_i$ be of order $n_i$ in $\\Bbb F_r^*$ and $\\gcd(n_i, n_j)=1$ for $1\\leq i \\neq j \\leq u$.\n  We define a cyclic code over $\\Bbb F_q$ by\n  $$\\mathcal C_{(q, m, n_1,n_2, ..., n_u)}=\\{c(a_1, a_2, ..., a_u) : a_1, a_2, ..., a_u \\in \\Bbb F_r\\},$$ where\n  $$c(a_1, a_2, ..., a_u)=({Tr}_{r/q}(\\sum_{i=1}^ua_ig_i^0), ..., {Tr}_{r/q}(\\sum_{i=1}^ua_ig_i^{n-1}))$$ and $n=n_1n_2... n_u$. In this paper, we present a method to compute the weights of $\\mathcal C_{(q, m, n_1,n_2, ..., n_u)}$. Further, we determine the weight dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5809","kind":"arxiv","version":2},"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"}