{"paper":{"title":"Self-Dual Cyclic and Quantum Codes Over Z2^{\\alpha} x (Z2 + uZ2)^{\\beta}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ismail Aydogdu, Taher Abualrub","submitted_at":"2017-11-09T10:05:57Z","abstract_excerpt":"In this paper we introduce self-dual cyclic and quantum codes over Z2^{\\alpha} x (Z2 + uZ2)^{\\beta}. We determine the conditions for any Z2Z2[u]-cyclic code to be self-dual, that is, C = C^{\\perp}. Since the binary image of a self-orthogonal Z2Z2[u]-linear code is also a self-orthogonal binary linear code, we introduce quantum codes over Z2^{\\alpha} x (Z2 + uZ2)^{\\beta}. Finally, we present some examples of self-dual cyclic and quantum codes that have good parameters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03307","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"}