DocumentCode
2888375
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
fYear
2011
fDate
28-30 Sept. 2011
Firstpage
1414
Lastpage
1415
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;
fLanguage
English
Publisher
ieee
Conference_Titel
Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on
Conference_Location
Monticello, IL
Print_ISBN
978-1-4577-1817-5
Type
conf
DOI
10.1109/Allerton.2011.6120333
Filename
6120333
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