Decoding linear error-correcting codes up to half the minimum distance with Gröbner bases

In: T. Mora and L. Perret and S. Sakata and M. Sala and C. Traverso ed., Working Title: "Gröbner Bases, Coding, and Cryptography". Proceedings of the Special Semester on Gröbner Bases, to appear, Volume 4, RISC Book Series (Springer, Heidelberg), 2009

Authors

• Stanislav Bulygin
• Ruud Pellikaan

Abstract

In this short note we show how one can solve the problem of decoding linear error-correcting codes up to half the minimum distance via solving a system of polynomial equations over a finite field. We also explicitly present the reduced Gröbner basis for the system considered.

BibTeX

 
@InCollection{ Bulygin.Pellikaan06decoding, 
   title = { Decoding linear error-correcting codes up to half the minimum distance with Gröbner bases }, 
   author = { Stanislav Bulygin and Ruud Pellikaan },  
   editor = { T. Mora and L. Perret and S. Sakata and M. Sala and C. Traverso }, 
   booktitle = { Working Title: "Gröbner Bases, Coding, and Cryptography" },  
   series = { Proceedings of the Special Semester on Gröbner Bases, to appear }, 
   volume = { 4 },     
   publisher = { RISC Book Series (Springer, Heidelberg) },      
   year = 2009, 
} 

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This publication belongs to the project KryFoVe.