{"paper":{"title":"$\\Theta_S-$cyclic codes over $A_k$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Ahmad Muchlis, Aleams Barra, Djoko Suprijanto, Intan Muchtadi-Alamsyah, Irwansyah, Olfa Yemen, Patrick Sol\\'e, Steven T. Dougherty","submitted_at":"2017-07-15T02:51:53Z","abstract_excerpt":"We study $\\Theta_S-$cyclic codes over the family of rings $A_k.$ We characterize $\\Theta_S-$cyclic codes in terms of their binary images. A family of Hermitian inner-products is defined and we prove that if a code is $\\Theta_S-$cyclic then its Hermitian dual is also $\\Theta_S-$cyclic. Finally, we give constructions of $\\Theta_S-$cyclic codes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04681","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"}