Computing coset leaders of binary codes

Abstract

We present an algorithm for computing the set of all coset leaders of a binary code $\mathcal C \subset \mathbb{F}_2^n$. The method is adapted from some of the techniques related to the computation of Gr\"obner representations associated with codes. The algorithm provides a Gr\"obner representation of the binary code and the set of coset leaders $\mathrm{CL}(\mathcal C)$. Its efficiency stands of the fact that its complexity is linear on the number of elements of $\mathrm{CL}(\mathcal C)$, which is smaller than exhaustive search in $\mathbb{F}_2^n$.