IJPAM: Volume 62, No. 4 (2010)
GROEBNER BASES FOR LINEAR CODES
Mehwish Saleemi
, Karl-Heinz Zimmermann
Institute of Computer Technology (E-13)
Hamburg University of Technology
Schwarzenbergstr. 95E, Hamburg, 21073, GERMANY
e-mail: chughtai@tuhh.de
e-mail: k.zimmermann@tuhh.de
, Karl-Heinz Zimmermann
Institute of Computer Technology (E-13)
Hamburg University of Technology
Schwarzenbergstr. 95E, Hamburg, 21073, GERMANY
e-mail: chughtai@tuhh.de
e-mail: k.zimmermann@tuhh.de
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