English

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 44-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