FGLM Techniques Applied to Linear Codes–An Algorithm for Decoding Linear Codes

M Borges-Quintana, MA Borges-Trenard… - Applicable Algebra in …, 2008 - Springer

In this paper we introduce a binomial ideal derived from a binary linear code. We present
some applications of a Gröbner basis of this ideal with respect to a total degree ordering. In …

被引用次数：68 相关文章所有 12 个版本

[PDF] arxiv.org

On a Gröbner bases structure associated to linear codes

M Borges-Quintana, MA Borges-Trenard… - Journal of Discrete …, 2007 - Taylor & Francis

We present a structure associated to the class of linear codes. The properties of that
structure are similar to some structures in the linear algebra techniques into the framework of …

被引用次数：36 相关文章所有 8 个版本

[PDF] arxiv.org

A general framework for applying FGLM techniques to linear codes

M Borges-Quintana, MA Borges-Trenard… - … Symposium on Applied …, 2006 - Springer

LNCS 3857 - A General Framework for Applying FGLM Techniques to Linear Codes Page 1 A
General Framework for Applying FGLM Techniques to Linear Codes M. Borges-Quintana1,⋆ …

被引用次数：18 相关文章所有 16 个版本

[PDF] academia.edu

[PDF][PDF] An FGLM method for decoding linear codes

MB Quintana, F Winkler, MAB Trenard - Proc. Encuentro de Algebra …, 2008 - academia.edu

A new algorithmic method is presented for the decoding process of a linear code. This
method has the flavor of the FGLM techniques that belong to the framework of the Gröbner …

被引用次数：2 相关文章所有 8 个版本

[PDF] oeaw.ac.at

[PDF][PDF] GBLA & Codes: Grobner basis associated with linear codes

M Borges-Quintana, MA Borges-Trenard… - ricamwww.ricam.oeaw.ac.at

The connection between Grobner bases and linear algebra comes from the very beginning,
ie from Buchberger's PhD thesis. In [6, 7] these techniques were generalized to different …

[引用][C] Using Groebner bases for determining the equivalence of linear codes and solving the decoding problem}}

M Borges-Quintana, MA Borges-Trenard… - 2005 - Research Institute for Symbolic …