IJPAM: Volume 84, No. 1 (2013)

COMPUTING GENERATING SETS FOR
QUATERNARY CODES USING GRÖBNER BASES

Natalia Dück1, Karl-Heinz Zimmermann2
1,2Hamburg University of Technology
Schwarzenbergstr. 95E, 21073 Hamburg, GERMANY


Abstract. Gröbner bases techniques can be used to compute a basis of a subspace of a finite-dimensional vector space over finite prime field given as a matrix kernel. Linear codes can be described as such subspaces and thus are an interesting area of application. Based on this, Gröbner bases techniques will be used to compute a generating set of a quaternary code given as a matrix kernel. In particular, if the quaternary code is free, the algorithm will provide a basis for the dual code.

Received: November 28, 2012

AMS Subject Classification: 13P10, 94B60

Key Words and Phrases: Gröbner basis, 4-module, linear code, quaternary code, dual code

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DOI: 10.12732/ijpam.v84i1.7 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 84
Issue: 1