English

Jacobi polynomials and design theory I

Combinatorics 2022-12-07 v3 Information Theory Group Theory math.IT Statistics Theory Statistics Theory

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.

Keywords

Cite

@article{arxiv.2207.10911,
  title  = {Jacobi polynomials and design theory I},
  author = {Himadri Shekhar Chakraborty and Tsuyoshi Miezaki and Manabu Oura and Yuuho Tanaka},
  journal= {arXiv preprint arXiv:2207.10911},
  year   = {2022}
}

Comments

23 pages

R2 v1 2026-06-25T01:08:21.448Z