{"paper":{"title":"An efficient method to construct self-dual cyclic codes of length $p^s$ over $\\mathbb{F}_{p^m}+u\\mathbb{F}_{p^m}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hai Q. Dinh, Somphong Jitman, Yonglin Cao, Yuan Cao","submitted_at":"2019-07-14T13:17:27Z","abstract_excerpt":"Let $p$ be an odd prime number, $\\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$ and $s$ a positive integer. Using some combinatorial identities, we obtain certain properties for Kronecker product of matrices over $\\mathbb{F}_p$ with a specific type. On that basis, we give an explicit representation and enumeration for all distinct self-dual cyclic codes of length $p^s$ over the finite chain ring $\\mathbb{F}_{p^m}+u\\mathbb{F}_{p^m}$ $(u^2=0)$. Moreover, We provide an efficient method to construct every self-dual cyclic code of length $p^s$ over $\\mathbb{F}_{p^m}+u\\mathbb{F}_{p^m}$ pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07107","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"}