Jacobi polynomials and harmonic weight enumerators of the first-order Reed--Muller codes and the extended Hamming codes
Tsuyoshi Miezaki, Akihiro Munemasa · arXiv (Cornell University) · 2023
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 $4$-designs in these codes.