Gröbner bases for lattices and an algebraic decoding algorithm

Abstract

In this paper we present Gröbner bases for lattices. Gröbner 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 Gröbner basis is assigned to Λ as the Gröbner basis of its label code L. Using this Gröbner basis an algebraic decoding algorithm is introduced.

DOI: 10.1109/Allerton.2011.6120333

Cite this paper

@article{Aliasgari2011Grx00F6bnerBF, title={Gröbner bases for lattices and an algebraic decoding algorithm}, author={Malihe Aliasgari and Mohammad-Reza Sadeghi and Daniel Panario}, journal={2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)}, year={2011}, pages={1414-1415} }