Properties of Weight Enumerator Polynomials

Abstract

The weight enumerator polynomial (noted w.e.p. in the sequel) is a helpful way of characterising a code. The minimum weight provides us with the minimum distance and hence with the error correction capacity. The McWilliams identities give us relations with the weight enumerator of the dual code. Also some other relations use the w.e.p. to compute various decoding probabilities. Finally the properties of the coefficients allow the deduction of some existence and non-existence theorems for linear codes. In this short paper we will first list some definitions and classical properties of w.e.p. and then give a few others.