{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T22:48:42Z","timestamp":1761864522082,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,10]],"date-time":"2023-04-10T00:00:00Z","timestamp":1681084800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University","doi-asserted-by":"publisher","award":["PNURSP2023R231"],"award-info":[{"award-number":["PNURSP2023R231"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Let Fq be a field of order q, where q is a power of an odd prime p, and \u03b1 and \u03b2 are two non-zero elements of Fq. The primary goal of this article is to study the structural properties of cyclic codes over a finite ring R=Fq[u1,u2]\/\u27e8u12\u2212\u03b12,u22\u2212\u03b22,u1u2\u2212u2u1\u27e9. We decompose the ring R by using orthogonal idempotents \u03941,\u03942,\u03943, and \u03944 as R=\u03941R\u2295\u03942R\u2295\u03943R\u2295\u03944R, and to construct quantum-error-correcting (QEC) codes over R. As an application, we construct some optimal LCD codes.<\/jats:p>","DOI":"10.3390\/axioms12040367","type":"journal-article","created":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T01:33:03Z","timestamp":1681176783000},"page":"367","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5162-7522","authenticated-orcid":false,"given":"Shakir","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7856-2861","authenticated-orcid":false,"given":"Amal S.","family":"Alali","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4414-1932","authenticated-orcid":false,"given":"Mohammad","family":"Jeelani","sequence":"additional","affiliation":[{"name":"Department of Computer Application, Faculty of Science, Integral University, Lucknow 226001, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9276-9989","authenticated-orcid":false,"given":"Muhammet","family":"Kurulay","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yildiz Technical University, Istanbul 34000, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0032-3400","authenticated-orcid":false,"given":"Elif Segah","family":"\u00d6ztas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Karamanoglu Mehmetbey University, Karaman 70100, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5525-6658","authenticated-orcid":false,"given":"Pushpendra","family":"Sharma","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1109\/18.681315","article-title":"Quantum error-correction via codes over GF(4)","volume":"44","author":"Calderbank","year":"1998","journal-title":"IEEE Trans. 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