  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 $\mathbb{F}_2^n$.
