Variants of Jacobi polynomials in coding theory

Himadri Shekhar Chakraborty*, Tsuyoshi Miezaki

*この研究の対応する著者

研究成果: Article査読

抄録

In this paper, we introduce the notion of the complete joint Jacobi polynomial of two linear codes of length n over Fq and Zk. We give the MacWilliams type identity for the complete joint Jacobi polynomials of codes. We also introduce the concepts of the average Jacobi polynomial and the average complete joint Jacobi polynomial over Fq and Zk. We give a representation of the average of the complete joint Jacobi polynomials of two linear codes of length n over Fq and Zk in terms of the compositions of n and its distribution in the codes. Further we present a generalization of the representation for the average of the (g+ 1) -fold complete joint Jacobi polynomials of codes over Fq and Zk. Finally, we give the notion of the average Jacobi intersection number of two codes.

本文言語English
ジャーナルDesigns, Codes, and Cryptography
DOI
出版ステータスAccepted/In press - 2021

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンスの応用
  • 離散数学と組合せ数学
  • 応用数学

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