{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219498825500963","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.