{"title":"On Cyclic and Negacyclic Codes of Length 8ps Over Fpm + uFpm","authors":"Saroj Rani","doi":"10.18311/jims/2020/23906","DOIUrl":null,"url":null,"abstract":"In this paper, we establish the algebraic structure of all cyclic and negacyclic codes of length 8<em>p</em><sup>s</sup> over the chain ring Fp<sup>m</sup> + uFp<sup>m</sup> in terms of their generator polynomials, where u<sup>2</sup> = 0 and s is a positive integer and p is an odd prime. We also find out the number of codewords in each of these cyclic codes. Besides this, we determine duals of cyclic codes and list self-dual cyclic and negacyclic codes of length 8<em>p</em><sup>s</sup> over Fp<sup>m</sup> + uFp<sup>m</sup>. Also, we determine μ and -constacyclic codes of length 8<em>p</em><sup>s</sup> over Fp<sup>m</sup> + uFp<sup>m</sup>.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Indian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18311/jims/2020/23906","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 3
Abstract
In this paper, we establish the algebraic structure of all cyclic and negacyclic codes of length 8ps over the chain ring Fpm + uFpm in terms of their generator polynomials, where u2 = 0 and s is a positive integer and p is an odd prime. We also find out the number of codewords in each of these cyclic codes. Besides this, we determine duals of cyclic codes and list self-dual cyclic and negacyclic codes of length 8ps over Fpm + uFpm. Also, we determine μ and -constacyclic codes of length 8ps over Fpm + uFpm.
期刊介绍：
The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.
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