Gröbner bases for lattices and an algebraic decoding algorithm


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} }