Title :
Gröbner bases for lattices and an algebraic decoding algorithm
Author :
Aliasgari, Malihe ; Sadeghi, Mohammad-Reza ; Panario, Daniel
Author_Institution :
Fac. of Math. & Comput. Sci., Amirkabir Univ. of Technol., Tehran, Iran
Abstract :
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.
Keywords :
algebraic codes; binary codes; decoding; lattice theory; linear codes; Grobner bases; algebraic decoding algorithm; binary linear codes; lattices; nonbinary group block codes; Block codes; Complexity theory; Lattices; Maximum likelihood decoding; Polynomials; Vectors; Gröbner bases; lattices; reduction;
Conference_Titel :
Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on
Conference_Location :
Monticello, IL
Print_ISBN :
978-1-4577-1817-5
DOI :
10.1109/Allerton.2011.6120333
