The structure of linear codes of constant weight

Abstract

In this paper we determine completely the structure of linear codes over ℤ/Nℤ of constant weight. Namely, we determine exactly which modules underlie linear codes of constant weight, and we describe the coordinate functionals involved. The weight functions considered are: Hamming weight, Lee weight, and Euclidean weight. We present a general uniqueness theorem for virtual linear codes of constant weight. Existence is settled on a case by case basis.