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.
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