Gröbner bases for lattices and an algebraic decoding algorithm
Malihe Aliasgari, Mohammad‐Reza Sadeghi, Daniel Panario · 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.