IJPAM: Volume 73, No. 4 (2011)

GROEBNER BASES FOR LINEAR CODES OVER GF(4)

Mehwish Saleemi$^1$, Karl-Heinz Zimmermann$^2$
$^{1,2}$Hamburg University of Technology
Hamburg, 21071, GERMANY


Abstract. A linear code over a prime field can be described by a binomial ideal in a polynomial ring given as the sum of a toric ideal and a nonprime ideal. A Groebner basis for such an ideal can be read off from a systematic generator matrix of the corresponding code. In this paper, a similar result will be presented for linear codes over $\GF(4)$. To this end, the extented alphabet $\GF(4)$ is dealt with by enlarging the polynomial ring.

Received: June 10, 2011

AMS Subject Classification: 13P10, 94B30

Key Words and Phrases: Groebner basis, linear code, binomial ideal, polynomial ring, toric ideal, nonprime ideal

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 73
Issue: 4