The weight formulation of a coset member for the one order Reed-Muller code has been obtained by Bool function and Hadamard transformation and the condition of two cosets with same weight hierarchy has been proved. 利用Bool函数和Hadamard变换给出一阶R&M码R(1,m)陪集中元素重量的表达式,同时给出了陪集重量分布相同的条件,并给出了严格的证明。
Coset Weight Hierarchy for One Order Reed-Muller Code 一阶R&M码陪集的重量分布