{"paper":{"title":"DNA Cyclic Codes Over The Ring $ \\F_2[u,v]/\\langle u^2-1,v^3-v,uv-vu \\rangle$","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Abhay Kumar Singh, Pratyush Kumar, Sukhamoy Pattanayak","submitted_at":"2015-11-12T15:56:21Z","abstract_excerpt":"In this paper, we mainly study the some structure of cyclic DNA codes of odd length over the ring $R = \\F_2[u,v]/\\langle u^2-1,v^3-v,uv-vu \\rangle$ which play an important role in DNA computing. We established a direct link between the element of ring $R$ and 64 codons by introducing a Gray map from $R$ to $R_1 = F_2 + uF_2, u^2 = 1$ where $R_1$ is the ring of four elements. The reverse constrain and the reverse-complement constraint codes over $R$ and $R_1$ are studied in this paper. Binary image of the cyclic codes over R also study. The paper concludes with some example on DNA codes obtaine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03937","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"}