雅可比多项式与设计理论1

SIAM J. Discret. Math. Pub Date : 2022-07-22 DOI:10.48550/arXiv.2207.10911

H. Chakraborty, T. Miezaki, M. Oura, Yuuho Tanaka

{"title":"雅可比多项式与设计理论1","authors":"H. Chakraborty, T. Miezaki, M. Oura, Yuuho Tanaka","doi":"10.48550/arXiv.2207.10911","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce the notion of Jacobi polynomials with multiple reference vectors of a code, and give the MacWilliams type identity for it. Moreover, we derive a formula to obtain the Jacobi polynomials using the Aronhold polarization operator. Finally, we describe some facts obtained from Type III and Type IV codes that interpret the relation between the Jacobi polynomials and designs.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Jacobi polynomials and design theory I\",\"authors\":\"H. Chakraborty, T. Miezaki, M. Oura, Yuuho Tanaka\",\"doi\":\"10.48550/arXiv.2207.10911\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce the notion of Jacobi polynomials with multiple reference vectors of a code, and give the MacWilliams type identity for it. Moreover, we derive a formula to obtain the Jacobi polynomials using the Aronhold polarization operator. Finally, we describe some facts obtained from Type III and Type IV codes that interpret the relation between the Jacobi polynomials and designs.\",\"PeriodicalId\":21749,\"journal\":{\"name\":\"SIAM J. Discret. Math.\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-07-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM J. Discret. Math.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2207.10911\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM J. Discret. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2207.10911","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 3

摘要

本文引入了一个码的多参考向量Jacobi多项式的概念，并给出了它的MacWilliams型恒等式。此外，我们还导出了利用Aronhold极化算子求Jacobi多项式的公式。最后，我们描述了从III型和IV型规范中获得的一些事实，这些事实解释了雅可比多项式与设计之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Jacobi polynomials and design theory I

In this paper, we introduce the notion of Jacobi polynomials with multiple reference vectors of a code, and give the MacWilliams type identity for it. Moreover, we derive a formula to obtain the Jacobi polynomials using the Aronhold polarization operator. Finally, we describe some facts obtained from Type III and Type IV codes that interpret the relation between the Jacobi polynomials and designs.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM J. Discret. Math.

自引率

0.00%

发文量