{"title":"用偏多环码构造量子码","authors":"Shikha Patel, O. Prakash","doi":"10.1109/ISIT50566.2022.9834659","DOIUrl":null,"url":null,"abstract":"This paper establishes the relation between skew polycyclic and skew sequential codes over a finite field. We prove with different induced vectors that right Θ-polycyclic codes are left Θ−1-polycyclic codes. Further, we characterize the condition under which a code is both left and right skew polycyclic with the same induced vectors. Moreover, an analogous study is also discussed for skew sequential codes. Further, to show the novelty of our work, many examples of \"MDS (Maximum Distance Separable)\" codes are provided. Finally, as an application, we construct quantum codes with good parameters from these codes.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"38 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantum codes construction from skew polycyclic codes\",\"authors\":\"Shikha Patel, O. Prakash\",\"doi\":\"10.1109/ISIT50566.2022.9834659\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper establishes the relation between skew polycyclic and skew sequential codes over a finite field. We prove with different induced vectors that right Θ-polycyclic codes are left Θ−1-polycyclic codes. Further, we characterize the condition under which a code is both left and right skew polycyclic with the same induced vectors. Moreover, an analogous study is also discussed for skew sequential codes. Further, to show the novelty of our work, many examples of \\\"MDS (Maximum Distance Separable)\\\" codes are provided. Finally, as an application, we construct quantum codes with good parameters from these codes.\",\"PeriodicalId\":348168,\"journal\":{\"name\":\"2022 IEEE International Symposium on Information Theory (ISIT)\",\"volume\":\"38 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2022 IEEE International Symposium on Information Theory (ISIT)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT50566.2022.9834659\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2022 IEEE International Symposium on Information Theory (ISIT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT50566.2022.9834659","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Quantum codes construction from skew polycyclic codes
This paper establishes the relation between skew polycyclic and skew sequential codes over a finite field. We prove with different induced vectors that right Θ-polycyclic codes are left Θ−1-polycyclic codes. Further, we characterize the condition under which a code is both left and right skew polycyclic with the same induced vectors. Moreover, an analogous study is also discussed for skew sequential codes. Further, to show the novelty of our work, many examples of "MDS (Maximum Distance Separable)" codes are provided. Finally, as an application, we construct quantum codes with good parameters from these codes.
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