{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:01:43Z","timestamp":1760058103640,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T00:00:00Z","timestamp":1741824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let R=Fpm[u,v]\u27e8u2,v2,uv\u2212vu\u27e9, where p is an odd prime and m is a positive integer. For a unit \u03b1 in R, \u03b1-constacyclic codes of length 2ps over R are ideals of R[x]\u27e8x2ps\u2212\u03b1\u27e9, where s is a positive integer. The structure of \u03b1-constacyclic codes are classified on the distinct cases for the unit \u03b1: when \u03b1 is a square in R and when it is not. In this paper, for all such \u03b1-constacyclic codes, the Hamming distances are determined using this structure. In addition, their symbol-pair distances are obtained. The symmetry property of Hamming and symbol-pair distances makes analysis easier and maintains consistency by guaranteeing that the distance between codewords is the same regardless of their order. As symmetry preserves invariant distance features across transformations, it improves error detection and correction.<\/jats:p>","DOI":"10.3390\/sym17030428","type":"journal-article","created":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T04:18:32Z","timestamp":1741839512000},"page":"428","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hamming and Symbol-Pair Distances of Constacyclic Codes of Length 2ps over Fpm[u,v]\u27e8u2,v2,uv\u2212vu\u27e9"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-2434-6778","authenticated-orcid":false,"given":"Divya","family":"Acharya","sequence":"first","affiliation":[{"name":"Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal 576104, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0749-8994","authenticated-orcid":false,"given":"Prasanna","family":"Poojary","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal 576104, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0631-0205","authenticated-orcid":false,"given":"Vadiraja G. R.","family":"Bhatta","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576104, India"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/BF01119999","article-title":"Semisimple cyclic and abelian codes. II","volume":"3","author":"Berman","year":"1967","journal-title":"Cybernetics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1109\/18.75250","article-title":"Repeated-root cyclic codes","volume":"37","author":"Lint","year":"1991","journal-title":"IEEE Trans. Inf. 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