{"paper":{"title":"Hulls of Cyclic Codes over $\\mathbb{Z}_4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.RA"],"primary_cat":"cs.IT","authors_text":"Ekkasit Sangwisut, Patanee Udomkavanich, Somphong Jitman","submitted_at":"2018-06-20T07:40:48Z","abstract_excerpt":"The hulls of linear and cyclic codes over finite fields have been of interest and extensively studied due to their wide applications. In this paper, the hulls of cyclic codes of length $n$ over the ring $\\mathbb{Z}_4$ have been focused on. Their characterization has been established in terms of the generators viewed as ideals in the quotient ring $\\mathbb{Z}_4[x]/\\langle x^n-1\\rangle$. An algorithm for computing the types of the hulls of cyclic codes of arbitrary odd length over $\\mathbb{Z}_4$ has been given. The average $2$-dimension $E(n)$ of the hulls of cyclic codes of odd length $n$ over "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07590","kind":"arxiv","version":2},"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"}