IJPAM: Volume 62, No. 4 (2010)

GROEBNER BASES FOR LINEAR CODES

Mehwish Saleemi$^1$, Karl-Heinz Zimmermann$^2$
$^{1,2}$Institute of Computer Technology (E-13)
Hamburg University of Technology
Schwarzenbergstr. 95E, Hamburg, 21073, GERMANY
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.Each linear code can be described by a binomial ideal given as the sum of a toric ideal and a non-prime ideal. In this paper, we show that each such binomial ideal has a very natural reduced Groebner basis which can be easily constructed from a systematic generator matrix of the code.

Received: June 30, 2010

AMS Subject Classification: 13P10, 94B05

Key Words and Phrases: commutative polynomial ring, binomial ideal, Groebner basis, linear code, encoding, decoding

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 62
Issue: 4