{"title":"有限域上序列码的多项式实现","authors":"M. Matsuoka","doi":"10.55937/sut/1342635577","DOIUrl":null,"url":null,"abstract":"In this paper we study the relation between polycyclic codes and sequential codes over finite fields. It is shown that, for a sequential code C ⊆ F, C is realized as an ideal in the quotient ring of the polynomial ring. Furthermore, we characterize the dual codes of polycyclic codes. AMS 2010 Mathematics Subject Classification. Primary 94B60; Secondary 94B15, 16D25.","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"36 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Polynomial realization of sequential codes over finite fields\",\"authors\":\"M. Matsuoka\",\"doi\":\"10.55937/sut/1342635577\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we study the relation between polycyclic codes and sequential codes over finite fields. It is shown that, for a sequential code C ⊆ F, C is realized as an ideal in the quotient ring of the polynomial ring. Furthermore, we characterize the dual codes of polycyclic codes. AMS 2010 Mathematics Subject Classification. Primary 94B60; Secondary 94B15, 16D25.\",\"PeriodicalId\":38708,\"journal\":{\"name\":\"SUT Journal of Mathematics\",\"volume\":\"36 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SUT Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.55937/sut/1342635577\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SUT Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.55937/sut/1342635577","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Polynomial realization of sequential codes over finite fields
In this paper we study the relation between polycyclic codes and sequential codes over finite fields. It is shown that, for a sequential code C ⊆ F, C is realized as an ideal in the quotient ring of the polynomial ring. Furthermore, we characterize the dual codes of polycyclic codes. AMS 2010 Mathematics Subject Classification. Primary 94B60; Secondary 94B15, 16D25.
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