Jacobi polynomials and design theory I

Himadri Shekhar Chakraborty, Tsuyoshi Miezaki, Manabu Oura, Yuuho Tanaka*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we introduce the notion of Jacobi polynomials of a code with multiple reference vectors, 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.

Original languageEnglish
Article number113339
JournalDiscrete Mathematics
Volume346
Issue number6
DOIs
Publication statusPublished - 2023 Jun

Keywords

  • Codes
  • Designs
  • Invariant theory
  • Jacobi polynomials

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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