Gröbner bases for lattices and an algebraic decoding algorithm

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 i...

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Bibliographic Details
Published in:2011 49th Annual Allerton Conference on Communication, Control, and Computing pp. 1414 - 1415
Main Authors: Aliasgari, Malihe, Sadeghi, Mohammad-Reza, Panario, Daniel
Format: Conference Proceeding
Language:English
Published: IEEE 01.09.2011
Subjects:
Block codes
Complexity theory
Gröbner bases
Lattices
Maximum likelihood decoding
Polynomials
reduction
Vectors
ISBN:1457718170, 9781457718175
Online Access:Get full text
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Summary: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.
ISBN:1457718170
9781457718175
DOI:10.1109/Allerton.2011.6120333