{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T18:16:40Z","timestamp":1772734600806,"version":"3.50.1"},"reference-count":21,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,28]],"date-time":"2023-01-28T00:00:00Z","timestamp":1674864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The main motivation of this work is to study and obtain some reversible and DNA codes of length n with better parameters. Here, we first investigate the structure of cyclic and skew cyclic codes over the chain ring R:=F4[v]\/\u27e8v3\u27e9. We show an association between the codons and the elements of R using a Gray map. Under this Gray map, we study reversible and DNA codes of length n. Finally, several new DNA codes are obtained that have improved parameters than previously known codes. We also determine the Hamming and the Edit distances of these codes.<\/jats:p>","DOI":"10.3390\/e25020239","type":"journal-article","created":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T03:56:27Z","timestamp":1675050987000},"page":"239","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["DNA Code from Cyclic and Skew Cyclic Codes over F4[v]\/\u27e8v3\u27e9"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6512-4229","authenticated-orcid":false,"given":"Om","family":"Prakash","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Patna, Bihar 801106, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9260-8344","authenticated-orcid":false,"given":"Ashutosh","family":"Singh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Patna, Bihar 801106, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8595-2400","authenticated-orcid":false,"given":"Ram Krishna","family":"Verma","sequence":"additional","affiliation":[{"name":"Department of Mathematics, SRM Institute of Science and Technology, Delhi-NCR Campus, Ghaziabad 201204, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4078-8301","authenticated-orcid":false,"given":"Patrick","family":"Sol\u00e9","sequence":"additional","affiliation":[{"name":"I2M, (CNRS, Aix-Marseille University, Centrale Marseille), 13009 Marseilles, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9433-7576","authenticated-orcid":false,"given":"Wei","family":"Cheng","sequence":"additional","affiliation":[{"name":"LTCI, T\u00e9l\u00e9com Paris (IP Paris), 19 Place Marguerite Perey, 91120 Palaiseau, France"},{"name":"Secure-IC S.A.S., 104 Boulevard du Montparnasse, 75014 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1126\/science.7973651","article-title":"Molecular computation of solutions to combinatorial problems","volume":"266","author":"Adleman","year":"1994","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1109\/18.312154","article-title":"The Z4-linearity of Kerdock, Preparata, Goethals, and related codes","volume":"40","author":"Hammons","year":"1994","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ling, S., and Xing, C. (2004). Coding Theory: A First Course, Cambridge University Press.","DOI":"10.1017\/CBO9780511755279"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1060","DOI":"10.1109\/18.841186","article-title":"On the Hamming distance of linear codes over a finite chain ring","volume":"46","author":"Norton","year":"2000","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/PL00012382","article-title":"On the structure of linear and cyclic codes over a finite chain ring","volume":"10","author":"Norton","year":"2000","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s10623-006-9034-5","article-title":"Cyclic codes over the rings Z2+uZ2 and Z2+uZ2+u2Z2","volume":"42","author":"Abualrub","year":"2007","journal-title":"Des. Codes Cryptogr."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s10623-015-0100-8","article-title":"Codes over F4+vF4 and some DNA applications","volume":"80","author":"Bayram","year":"2016","journal-title":"Des. Codes Cryptogr."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s00200-013-0188-x","article-title":"Construction of cyclic codes over F2+uF2 for DNA computing","volume":"24","author":"Guenda","year":"2013","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40314-021-01635-y","article-title":"Reversible cyclic codes over some finite rings and their application to DNA codes","volume":"40","author":"Prakash","year":"2021","journal-title":"Comput. Appl. Math."},{"key":"ref_10","first-page":"52","article-title":"Reversible cyclic codes over a class of chain rings and their application to DNA codes","volume":"6","author":"Prakash","year":"2022","journal-title":"Int. J. Inf. Coding Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"83","DOI":"10.3934\/amc.2017004","article-title":"DNA cyclic codes over rings","volume":"11","author":"Bennenni","year":"2017","journal-title":"Adv. Math. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s40304-019-00188-1","article-title":"On Cyclic DNA Codes Over F2+uF2+u2F2","volume":"9","author":"Mostafanasab","year":"2021","journal-title":"Commun. Math. Stat."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1016\/j.camwa.2011.12.029","article-title":"Cyclic codes over F2[u]\/(u4\u22121) and applications to DNA codes","volume":"63","author":"Yildiz","year":"2012","journal-title":"Comput. Math. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"77528","DOI":"10.1109\/ACCESS.2020.2989203","article-title":"DNA Codes Over the Ring F4[u]\/\u2329u3\u232a","volume":"8","author":"Liu","year":"2020","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1644","DOI":"10.1016\/j.jsc.2007.11.008","article-title":"Coding with skew polynomial rings","volume":"44","author":"Boucher","year":"2009","journal-title":"J. Symbolic Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"39","DOI":"10.3934\/amc.2012.6.39","article-title":"Skew constacyclic codes over finite chain rings","volume":"6","author":"Jitman","year":"2012","journal-title":"Adv. Math. Commun."},{"key":"ref_17","first-page":"10","article-title":"Skew cyclic codes of arbitrary length","volume":"2","author":"Siap","year":"2011","journal-title":"Int. J. Inf. Coding Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s00200-017-0325-z","article-title":"Reversible DNA codes using skew polynomial rings","volume":"28","author":"Gursoy","year":"2017","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.13069\/jacodesmath.864902","article-title":"Reversible DNA codes from skew cyclic codes over a ring of order 256","volume":"8","author":"Cengellenmis","year":"2021","journal-title":"J. Algebra Comb. Discret. Struct. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1006\/jsco.1996.0125","article-title":"The Magma algebra system I: The user language","volume":"24","author":"Bosma","year":"1997","journal-title":"J. Symbolic Comput."},{"key":"ref_21","unstructured":"Limbachiya, D., Rao, B., and Gupta, M.K. (2016). The art of DNA strings: Sixteen years of DNA coding theory. arXiv."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/2\/239\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:17:52Z","timestamp":1760120272000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/2\/239"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,28]]},"references-count":21,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["e25020239"],"URL":"https:\/\/doi.org\/10.3390\/e25020239","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,28]]}}}