{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T20:26:52Z","timestamp":1778099212067,"version":"3.51.4"},"reference-count":6,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001501","name":"University Grants Commission","doi-asserted-by":"publisher","award":["Sr. No. 2121540952"],"award-info":[{"award-number":["Sr. No. 2121540952"]}],"id":[{"id":"10.13039\/501100001501","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001501","name":"University Grants Commission","doi-asserted-by":"publisher","award":["Ref. No. 20\/12\/2015(ii)EU-V"],"award-info":[{"award-number":["Ref. 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Appl."],"published-print":{"date-parts":[[2018,8]]},"abstract":"<jats:p> In this paper, we study [Formula: see text]-constacyclic codes over the ring [Formula: see text], where [Formula: see text] for [Formula: see text] and [Formula: see text], respectively. We define some new Gray maps from [Formula: see text] to the copies of [Formula: see text]. It is shown that Gray images of [Formula: see text]-constacyclic codes over [Formula: see text] are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over [Formula: see text]. Further, we extend and obtain cyclic codes, [Formula: see text]-constacyclic codes and permutation equivalent to quasi-cyclic codes over [Formula: see text], respectively, as Gray images of skew [Formula: see text]-constacyclic codes over [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830918500568","type":"journal-article","created":{"date-parts":[[2018,6,18]],"date-time":"2018-06-18T23:09:41Z","timestamp":1529363381000},"page":"1850056","source":"Crossref","is-referenced-by-count":4,"title":["A study of constacyclic codes over the ring \u21244[u]\/\u3008u2 \u2212 3\u3009"],"prefix":"10.1142","volume":"10","author":[{"given":"Tushar","family":"Bag","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Habibul","family":"Islam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6512-4229","authenticated-orcid":false,"given":"Om","family":"Prakash","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ashish K.","family":"Upadhyay","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,7,30]]},"reference":[{"key":"S1793830918500568BIB001","first-page":"195","volume":"38","author":"Abualrub T.","year":"2007","journal-title":"Australas. 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