{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:10:08Z","timestamp":1753881008802,"version":"3.41.2"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"asghar"},{"DOI":"10.13039\/501100004160","name":"Mazandaran University of Medical Sciences","doi-asserted-by":"publisher","award":["123"],"award-info":[{"award-number":["123"]}],"id":[{"id":"10.13039\/501100004160","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:p> A perfect [Formula: see text]-code in a graph [Formula: see text] is a subset [Formula: see text] of [Formula: see text] such that every vertex of [Formula: see text] is at a distance not more than [Formula: see text], to exactly one vertex of [Formula: see text]. In this paper, we present a new family of perfect [Formula: see text]-codes in Cayley graphs of groups. We proposed the role of the subgroups of a group to create perfect [Formula: see text]-codes by restricting the elements of the left transversal of the subgroups in the given group. Also, we introduce a new decoding algorithm for the all of perfect [Formula: see text]-codes in Cayley graphs. These codes are able to correct every [Formula: see text]-error pattern. <\/jats:p>","DOI":"10.1142\/s1793830921501019","type":"journal-article","created":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T03:18:57Z","timestamp":1612495137000},"source":"Crossref","is-referenced-by-count":0,"title":["Perfect t-codes in Cayley graphs of groups"],"prefix":"10.1142","volume":"14","author":[{"given":"Neda","family":"Bagheri","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Mazandaran, Babolsar, Iran"}]},{"given":"A.","family":"Asghar Talebi Rostami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Mazandaran, Babolsar, Iran"}]}],"member":"219","published-online":{"date-parts":[[2021,4,19]]},"reference":[{"key":"S1793830921501019BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(73)90042-7"},{"key":"S1793830921501019BIB002","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2517069"},{"key":"S1793830921501019BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0163-9"},{"key":"S1793830921501019BIB004","doi-asserted-by":"publisher","DOI":"10.1137\/0118025"},{"volume-title":"A First Course in Coding Theory","year":"1986","author":"Hill R.","key":"S1793830921501019BIB005"},{"key":"S1793830921501019BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.03.019"},{"key":"S1793830921501019BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2008.04.007"},{"key":"S1793830921501019BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2013.10.010"},{"key":"S1793830921501019BIB009","doi-asserted-by":"publisher","DOI":"10.1137\/17M1129532"},{"key":"S1793830921501019BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-013-9893-5"},{"key":"S1793830921501019BIB011","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2010.5513673"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921501019","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,7]],"date-time":"2022-03-07T11:35:27Z","timestamp":1646652927000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921501019"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,19]]},"references-count":11,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["10.1142\/S1793830921501019"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921501019","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2021,4,19]]},"article-number":"2150101"}}