一类t权码及其应用

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications Pub Date : 2023-11-03 DOI:10.1142/s0219498825500963

J. Prabu, J. Mahalakshmi, S. Santhakumar

{"title":"一类t权码及其应用","authors":"J. Prabu, J. Mahalakshmi, S. Santhakumar","doi":"10.1142/s0219498825500963","DOIUrl":null,"url":null,"abstract":"In this paper, we constructed a class of [Formula: see text]-weight linear codes over [Formula: see text] under the homogeneous weight metric by their generator matrices, where [Formula: see text] and [Formula: see text] The Gray images of some class of these codes over [Formula: see text] are [Formula: see text]-ary nonlinear codes, which have the same weight distributions as that of the two-weight [Formula: see text]-ary linear codes of type SU1 in the sense of [R. Calderbank and W. M. Kantor, The geometry of two-weight codes, Bull. London Math. Soc. 18(2) (1986) 97–122]. Also, we obtained the minimum distance of the dual codes of the constructed codes. Further, we discussed some optimal linear codes over [Formula: see text] with respect to Plotkin-type bound from the constructed codes when [Formula: see text] Furthermore, we investigated the applications in strongly regular graphs and secret sharing schemes.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A class of <i>t</i>-weight codes and its applications\",\"authors\":\"J. Prabu, J. Mahalakshmi, S. Santhakumar\",\"doi\":\"10.1142/s0219498825500963\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we constructed a class of [Formula: see text]-weight linear codes over [Formula: see text] under the homogeneous weight metric by their generator matrices, where [Formula: see text] and [Formula: see text] The Gray images of some class of these codes over [Formula: see text] are [Formula: see text]-ary nonlinear codes, which have the same weight distributions as that of the two-weight [Formula: see text]-ary linear codes of type SU1 in the sense of [R. Calderbank and W. M. Kantor, The geometry of two-weight codes, Bull. London Math. Soc. 18(2) (1986) 97–122]. Also, we obtained the minimum distance of the dual codes of the constructed codes. Further, we discussed some optimal linear codes over [Formula: see text] with respect to Plotkin-type bound from the constructed codes when [Formula: see text] Furthermore, we investigated the applications in strongly regular graphs and secret sharing schemes.\",\"PeriodicalId\":54888,\"journal\":{\"name\":\"Journal of Algebra and Its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra and Its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219498825500963\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra and Its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219498825500963","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文通过生成矩阵在齐次权测度下构造了一类[公式:见文]上的[公式:见文]-权线性码，其中[公式:见文]和[公式:见文]这类码在[公式:见文]上的灰度图像为[公式:见文]-任意非线性码，其权重分布与[R]意义上的双权[公式:见文]-任意线性码的权重分布相同。卡尔德班克和W. M.坎特，二权码的几何性质，第2卷。伦敦数学。Soc. 18(2)(1986) 97-122]。同时，我们得到了所构造码的对偶码的最小距离。在此基础上，我们进一步讨论了[公式:见文]构造的码在[公式:见文]上关于plotkin型界的一些最优线性码，并研究了它们在强正则图和秘密共享方案中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A class of t-weight codes and its applications

In this paper, we constructed a class of [Formula: see text]-weight linear codes over [Formula: see text] under the homogeneous weight metric by their generator matrices, where [Formula: see text] and [Formula: see text] The Gray images of some class of these codes over [Formula: see text] are [Formula: see text]-ary nonlinear codes, which have the same weight distributions as that of the two-weight [Formula: see text]-ary linear codes of type SU1 in the sense of [R. Calderbank and W. M. Kantor, The geometry of two-weight codes, Bull. London Math. Soc. 18(2) (1986) 97–122]. Also, we obtained the minimum distance of the dual codes of the constructed codes. Further, we discussed some optimal linear codes over [Formula: see text] with respect to Plotkin-type bound from the constructed codes when [Formula: see text] Furthermore, we investigated the applications in strongly regular graphs and secret sharing schemes.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Algebra and Its Applications 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

226

审稿时长

4-8 weeks

期刊介绍： The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.