Gröbner bases for lattices and an algebraic decoding algorithm - Aliasgari, Malihe; Sadeghi, Mohammad-Reza; Panario, Daniel (2011 49th Annual Allerton Conference on Communication, Control, and Computing, 2011)
In this paper we present Grobner bases for lattices. Grobner bases for binary linear codes were introduced by Borges et al. [3]. We extend their work to non-binary group block codes. Given a lattice Λ and its associated label code L, which is a group code, we define an ideal for L. A Grobner basis is assigned to Λ as the Grobner basis of its label code L. Using this Grobner basis an algebraic decoding algorithm is introduced.