{"paper":{"title":"On the weight distributions of several classes of cyclic codes from APN monomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chunlei Li, Cunsheng Ding, Nian Li, Tor Helleseth","submitted_at":"2013-08-27T14:48:52Z","abstract_excerpt":"Let $m\\geq 3$ be an odd integer and $p$ be an odd prime. % with $p-1=2^rh$, where $h$ is an odd integer.\n  In this paper, many classes of three-weight cyclic codes over $\\mathbb{F}_{p}$ are presented via an examination of the condition for the cyclic codes $\\mathcal{C}_{(1,d)}$ and $\\mathcal{C}_{(1,e)}$, which have parity-check polynomials $m_1(x)m_d(x)$ and $m_1(x)m_e(x)$ respectively, to have the same weight distribution, where $m_i(x)$ is the minimal polynomial of $\\pi^{-i}$ over $\\mathbb{F}_{p}$ for a primitive element $\\pi$ of $\\mathbb{F}_{p^m}$. %For $p=3$, the duals of five classes of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5885","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"}