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 Gröbner representations associated with codes. The algorithm provides a Gröbner 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 ${\mathbb{F}}_2^n$.

Submitted to Designs, Codes and Cryptography