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.

翻译：本文针对格子码提出了两种算法。第一种算法计算了格子标签码的扩充完全Gröbner基，该基支持与全次数序关联的所有项序，能够提供关于该格子标签码的信息。第二种算法是一种译码算法，它利用格子标签码的扩充完全Gröbner基进行单项式约简，从而为给定的向量提供构成最近向量问题解候选的所有格向量。