Jacobi polynomials and harmonic weight enumerators of the first-order Reed--Muller codes and the extended Hamming codes
Combinatorics
2024-01-03 v4 Number Theory
Abstract
In the present paper, we give harmonic weight enumerators and Jacobi polynomials for the first-order Reed--Muller codes and the extended Hamming codes. As a corollary, we show the nonexistence of combinatorial -designs in these codes.
Keywords
Cite
@article{arxiv.2303.16349,
title = {Jacobi polynomials and harmonic weight enumerators of the first-order Reed--Muller codes and the extended Hamming codes},
author = {Tsuyoshi Miezaki and Akihiro Munemasa},
journal= {arXiv preprint arXiv:2303.16349},
year = {2024}
}
Comments
9 pages, corrected typo