{"paper":{"title":"Hermitian Self-Dual Cyclic Codes of Length $p^a$ over $GR(p^2,s)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.RA","authors_text":"Ekkasit Sangwisut, San Ling, Somphong Jitman","submitted_at":"2014-01-26T10:28:36Z","abstract_excerpt":"In this paper, we study cyclic codes over the Galois ring ${\\rm GR}({p^2},s)$. The main result is the characterization and enumeration of Hermitian self-dual cyclic codes of length $p^a$ over ${\\rm GR}({p^2},s)$. Combining with some known results and the standard Discrete Fourier Transform decomposition, we arrive at the characterization and enumeration of Euclidean self-dual cyclic codes of any length over ${\\rm GR}({p^2},s)$. Some corrections to results on Euclidean self-dual cyclic codes of even length over $\\mathbb{Z}_4$ in Discrete Appl. Math. 128, (2003), 27 and Des. Codes Cryptogr. 39, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6634","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"}