{"title":"环上的齐次权$\\mathfrak{R}_{5,3}=\\mathbb{F}_5+u_1\\mathbb{F}_5+u_2\\mathbb{F}_5+u_3\\mathbb{F}_5$","authors":"O. Haddouche, H. Zekraoui, K. Chatouh","doi":"10.37418/amsj.11.11.11","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate linear codes over the ring $ \\mathfrak{R}_{5,3}=\\mathbb{F}_{5}+u_{1}\\mathbb{F}_{5}+u_{2}\\mathbb{F}_{5}+u_{3}\\mathbb{F}_{5} $, and we determine the homogeneous weight of this ring, to derive some properties corresponding to these codes.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"34 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hommogenous weights on the ring $\\\\mathfrak{R}_{5,3}=\\\\mathbb{F}_5+u_1\\\\mathbb{F}_5+u_2\\\\mathbb{F}_5+u_3\\\\mathbb{F}_5$\",\"authors\":\"O. Haddouche, H. Zekraoui, K. Chatouh\",\"doi\":\"10.37418/amsj.11.11.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we investigate linear codes over the ring $ \\\\mathfrak{R}_{5,3}=\\\\mathbb{F}_{5}+u_{1}\\\\mathbb{F}_{5}+u_{2}\\\\mathbb{F}_{5}+u_{3}\\\\mathbb{F}_{5} $, and we determine the homogeneous weight of this ring, to derive some properties corresponding to these codes.\",\"PeriodicalId\":231117,\"journal\":{\"name\":\"Advances in Mathematics: Scientific Journal\",\"volume\":\"34 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics: Scientific Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37418/amsj.11.11.11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics: Scientific Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37418/amsj.11.11.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hommogenous weights on the ring $\mathfrak{R}_{5,3}=\mathbb{F}_5+u_1\mathbb{F}_5+u_2\mathbb{F}_5+u_3\mathbb{F}_5$
In this paper, we investigate linear codes over the ring $ \mathfrak{R}_{5,3}=\mathbb{F}_{5}+u_{1}\mathbb{F}_{5}+u_{2}\mathbb{F}_{5}+u_{3}\mathbb{F}_{5} $, and we determine the homogeneous weight of this ring, to derive some properties corresponding to these codes.
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