{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:23:27Z","timestamp":1760149407338,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,2]],"date-time":"2023-08-02T00:00:00Z","timestamp":1690934400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The key objective of this paper is to study the cyclic codes over mixed alphabets on the structure of FqPQ, where P=Fq[v]\u27e8v3\u2212\u03b122v\u27e9 and Q=Fq[u,v]\u27e8u2\u2212\u03b112,v3\u2212\u03b122v\u27e9 are nonchain finite rings and \u03b1i is in Fq\/{0} for i\u2208{1,2}, where q=pm with m\u22651 is a positive integer and p is an odd prime. Moreover, with the applications, we obtain better and new quantum error-correcting (QEC) codes. For another application over the ring P, we obtain several optimal codes with the help of the Gray image of cyclic codes.<\/jats:p>","DOI":"10.3390\/e25081161","type":"journal-article","created":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T11:08:43Z","timestamp":1691060923000},"page":"1161","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Optimal and Quantum Code Construction from Cyclic Codes over \r\nFqPQ with Applications"],"prefix":"10.3390","volume":"25","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\/0000-0002-5525-6658","authenticated-orcid":false,"given":"Pushpendra","family":"Sharma","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India"}]},{"given":"Kok Bin","family":"Wong","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia"}]},{"given":"Elif Segah","family":"\u00d6ztas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kamil Ozdag Science Faculty, Karamanoglu Mehmetbey University, Karaman 70100, Turkey"}]},{"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 226026, India"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,2]]},"reference":[{"key":"ref_1","unstructured":"Prange, E. 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