In this short note we show how one can decode 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.
|Title of host publication
|Gröbner Bases, Coding, and Cryptography
|M. Sala, T. Mora, L. Perret, S. Sakata, C. Traverso
|Place of Publication
|Published - 2009
|Texts and Monographs in Symbolic Computation