{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T04:43:30Z","timestamp":1774154610527,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"DOI":"10.13039\/501100004704","name":"National Research Council of Thailand","doi-asserted-by":"crossref","award":["NRCT5-RSA63011-05"],"award-info":[{"award-number":["NRCT5-RSA63011-05"]}],"id":[{"id":"10.13039\/501100004704","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,10]]},"abstract":"<jats:p> In this paper, we develop a theory for constructing cyclic codes of odd length over the ring [Formula: see text], where [Formula: see text], which plays an important role in DNA computing. A direct link between the elements of [Formula: see text] and the [Formula: see text] codons used in the amino acids of the living organisms is established. Then, we investigate reversible cyclic codes and reversible complement cyclic codes of odd length over [Formula: see text]. Moreover, we give some properties of binary images of the codons under the Gray map. Finally, two examples of cyclic codes over [Formula: see text] with their minimum Hamming distance will be studied as well. <\/jats:p>","DOI":"10.1142\/s1793830922501579","type":"journal-article","created":{"date-parts":[[2022,9,16]],"date-time":"2022-09-16T12:10:01Z","timestamp":1663330201000},"source":"Crossref","is-referenced-by-count":1,"title":["Reversible complement cyclic codes over \u21244 + u\u21244 + v\u21244 for DNA computing"],"prefix":"10.1142","volume":"15","author":[{"given":"Chakkrid","family":"Klin-Eam","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand"}]},{"given":"Wateekorn","family":"Sriwirach","sequence":"additional","affiliation":[{"name":"Office of Agricultural Economics, Ministry of Agriculture and Cooperatives, Bangkok 10900, Thailand"}]}],"member":"219","published-online":{"date-parts":[[2022,10,20]]},"reference":[{"issue":"4","key":"S1793830922501579BIB001","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1016\/j.jfranklin.2006.02.009","volume":"343","author":"Abualrub T.","year":"2006","journal-title":"J. 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