{"title":"Reed-Muller码的代数结构","authors":"Harinaivo Andriatahiny","doi":"10.26493/2590-9770.1417.02a","DOIUrl":null,"url":null,"abstract":"It is known that the Reed-Muller codes over a prime field may be described as the radical powers of a modular group algebra. In this paper, we give a new proof of the same result in a quotient of a polynomial ring. Special elements in a prime field are studied. An interpolation polynomial is introduced in order to characterize the coefficients of the Jennings polynomials.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"193 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On algebraic structure of the Reed-Muller codes\",\"authors\":\"Harinaivo Andriatahiny\",\"doi\":\"10.26493/2590-9770.1417.02a\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is known that the Reed-Muller codes over a prime field may be described as the radical powers of a modular group algebra. In this paper, we give a new proof of the same result in a quotient of a polynomial ring. Special elements in a prime field are studied. An interpolation polynomial is introduced in order to characterize the coefficients of the Jennings polynomials.\",\"PeriodicalId\":236892,\"journal\":{\"name\":\"Art Discret. Appl. Math.\",\"volume\":\"193 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Art Discret. Appl. Math.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26493/2590-9770.1417.02a\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Art Discret. Appl. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26493/2590-9770.1417.02a","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
It is known that the Reed-Muller codes over a prime field may be described as the radical powers of a modular group algebra. In this paper, we give a new proof of the same result in a quotient of a polynomial ring. Special elements in a prime field are studied. An interpolation polynomial is introduced in order to characterize the coefficients of the Jennings polynomials.
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