{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:12:35Z","timestamp":1760058755501,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T00:00:00Z","timestamp":1745452800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2023A1515110501","QN202441"],"award-info":[{"award-number":["2023A1515110501","QN202441"]}]},{"name":"Zhaoqing University Research Fund youth project","award":["2023A1515110501","QN202441"],"award-info":[{"award-number":["2023A1515110501","QN202441"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Symbol-pair codes are a class of block codes with symbol-pair metrics designed to protect against pair errors that may occur in high-density data storage systems. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that they can attain the highest pair-error correctability within the same code length and code size. Constructing MDS symbol-pair codes is one of the main topics in symbol-pair code research. In this paper, we investigate and characterize the symbol-pair distances of constacyclic codes of arbitrary lengths over finite fields and finite chain rings. Using the characterization of the symbol-pair distance, we present three new classes of MDS symbol-pair constacyclic codes that exhibit large minimum distances.<\/jats:p>","DOI":"10.3390\/axioms14050327","type":"journal-article","created":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T04:04:50Z","timestamp":1745467490000},"page":"327","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Symbol-Pair Distances of a Class of Repeated-Root Constacyclic Codes of Length nps over Fpm and over Fpm+uFpm"],"prefix":"10.3390","volume":"14","author":[{"given":"Wei","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Mathematics, Foshan University, Foshan 528000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3630-368X","authenticated-orcid":false,"given":"Weixian","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics, Foshan University, Foshan 528000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"8011","DOI":"10.1109\/TIT.2011.2164891","article-title":"Codes for symbol-pair read channels","volume":"57","author":"Cassuto","year":"2011","journal-title":"IEEE Trans. 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