A Note on Weight Enumerators of Linear Self-Dual Codes
N. Lomadze · Georgian Mathematical Journal · 1998
Abstract. A partial description of (complete) weight enumerators of linear self-dual codes is given. 0. Let F = Z/pZ, where p is a prime number. If C is a linear code on F of length n, i.e., a linear subspace in F n, then its (complete) weight enumerator WC is defined to be u∈C a∈F x sa(u) a. Here xa, a ∈ F are indeterminates; sa(u) denotes the number of entries of u in C equal to a. This is a homogeneous polynomial in p indeterminates of degree n. Define the additive character ψ of F by and let k ↦→ e 2πi p) k, k ∈ F, A = 1 () √ ψ(ij)