{"paper":{"title":"The weight distribution of a family of p-ary cyclic codes","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":"2014-05-21T02:03:49Z","abstract_excerpt":"Let m, k be positive integers, p be an odd prime and $\\pi $ be a primitive element of $\\mathbb{F}_{p^m}$. In this paper, we determine the weight distribution of a family of cyclic codes $\\mathcal{C}_t$ over $\\mathbb{F}_p$, whose duals have two zeros $\\pi^{-t}$ and $-\\pi^{-t}$, where $t$ satisfies $t\\equiv \\frac{p^k+1}{2}p^\\tau \\ ({\\rm mod}\\ \\frac{p^m-1}{2}) $ for some $\\tau \\in \\{0,1,\\cdots, m-1\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5278","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"}