  In this work, two algorithms are developed related to lattice codes. In the
first one, an extended complete Gr\"obner basis is computed for the label code
of a lattice. This basis supports all term orderings associated with a total
degree order offering information about de label code of the lattice. The
second one is a decoding algorithm that uses an extended complete Gr\"obner
basis of the label code of the lattice for monomial reduction, this provides
all the lattice vectors that constitute candidates for the solution of the
Close Vector Problem for a given vector.
