Variants of Jacobi polynomials in coding theory

Himadri Shekhar Chakraborty*, Tsuyoshi Miezaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
JournalDesigns, Codes, and Cryptography
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Codes
  • Jacobi polynomials
  • Weight enumerators

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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