@inproceedings{1d290ce9844542c99f192a2ebf97b677,
title = "Gr{\"o}bner bases for lattices and an algebraic decoding algorithm",
abstract = "In this paper we present Gr{\"o}bner bases for lattices. Gr{\"o}bner 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 Gr{\"o}bner basis is assigned to Λ as the Gr{\"o}bner basis of its label code L. Using this Gr{\"o}bner basis an algebraic decoding algorithm is introduced.",
keywords = "Gr{\"o}bner bases, lattices, reduction",
author = "Malihe Aliasgari and Sadeghi, {Mohammad Reza} and Daniel Panario",
year = "2011",
doi = "10.1109/Allerton.2011.6120333",
language = "English",
isbn = "9781457718168",
series = "2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011",
pages = "1414--1415",
booktitle = "2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011",
note = "2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011 ; Conference date: 28-09-2011 Through 30-09-2011",
}