{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:56:31Z","timestamp":1760147791021,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T00:00:00Z","timestamp":1677628800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Let p\u22603 be any prime. In this paper, we compute symbol-pair distance of all \u03b3-constacyclic codes of length 3ps over the finite commutative chain ring R=Fpm+uFpm, where \u03b3 is a unit of R which is not a cube in Fpm. We give the necessary and sufficient condition for a symbol-pair \u03b3-constacyclic code to be an MDS symbol-pair code. Using that, we provide all MDS symbol-pair \u03b3-constacyclic codes of length 3ps over R. Some examples of the symbol-pair distance of \u03b3-constacyclic codes of length 3ps over R are provided.<\/jats:p>","DOI":"10.3390\/axioms12030254","type":"journal-article","created":{"date-parts":[[2023,3,2]],"date-time":"2023-03-02T02:10:59Z","timestamp":1677723059000},"page":"254","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On Symbol-Pair Distance of a Class of Constacyclic Codes of Length 3ps over Fpm+uFpm"],"prefix":"10.3390","volume":"12","author":[{"given":"Hai Q.","family":"Dinh","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiep L.","family":"Thi","sequence":"additional","affiliation":[{"name":"Faculty of Education, Thu Dau Mot University, Binh Duong 75000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-9379-4414","authenticated-orcid":false,"given":"Roengchai","family":"Tansuchat","sequence":"additional","affiliation":[{"name":"Faculty of Economics, Chiang Mai University, Chiang Mai 52000, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3306","DOI":"10.1109\/TIT.2004.838109","article-title":"A mass formula and rank of Z4 cyclic codes of length 2e","volume":"50","author":"Abualrub","year":"2004","journal-title":"IEEE Trans. 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