Computing Gröbner bases associated with lattices

We specialize Möller's algorithm to the computation ofGröbner bases related to lattices. We give the complexityanalysis of our algorithm. Then we provide experiments showingthat our algorithm is more efficient than Buchberger's algorithmfor computing the associated Gröbner bases. Furthermore weshow that the binomial ideal associated to the lattice can beconstructed from a set of binomials associated with a set ofgenerators of the corresponding label code. This result ispresented in a general way by means of three idealconstructions associated with group codes that constitute thesame ideal. This generalizes earlier results for specific casesof group codes such as linear codes, codes over ${\mathbb Z}_m$and label codes of lattices.