{"paper":{"title":"Weight distributions of all irreducible $\\mu$-constacyclic codes of length $\\ell^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Manjit Singh","submitted_at":"2018-06-27T02:55:07Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be a finite field of order $q$ and integer $n\\ge 1$. Let $\\ell$ be a prime such that $\\ell^k|(q-1)$ for some integer $k\\ge 1$ and $\\mu$ be an element of order $\\ell^k$ in $\\mathbb{F}_q$. In this paper, we determine the weight distributions of all irreducible $\\mu$-constacyclic codes of length $\\ell^n$ over $\\mathbb{F}_q$. Explicit expressions for the generator polynomials and codewords of these codes are also obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10600","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"}