Author(s)： Michio Ozeki and Katsushi Waki

J. Math-for-Ind. 3A (2011) 1-20.

• File： JMI2011A-1.pdf (188KB)

Abstract
In this paper we determine the complete coset weight distributions of the second order Reed-Muller code $RM(2, 6)$ of length 64. Our method fully uses the interaction between the Jacobi polynomials for the code $RM(2, 6)$ and those of the dual code $RM(3, 6)$. The method also employs the group theoretic reduction processes to diminish the runtimes of computing the Jacobi polynomials for the code $RM(2, 6)$ in great effect.

Keyword(s).　 second order Reed-Muller code of length 64, coset weight distributions, Jacobi polynomials