{"paper":{"title":"Construction of cyclic DNA codes over the Ring $\\Z_4[u]/\\langle u^2-1 \\rangle $ Based on the deletion distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Abhay Kumar Singh, Sukhamoy Pattanayak","submitted_at":"2016-03-13T18:00:34Z","abstract_excerpt":"In this paper, we develop the theory for constructing DNA cyclic codes of odd length over $R=\\Z_4[u]/\\langle u^2-1 \\rangle$ based on the deletion distance. Firstly, we relate DNA pairs with a special 16 elements of ring $R$. Cyclic codes of odd length over $R$ satisfy the reverse constraint and the reverse-complement constraint are discussed in this paper. We also study the $GC$-content of these codes and their deletion distance. The paper concludes with some examples of cyclic DNA codes with $GC$-content and their respective deletion distance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04055","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"}