IJPAM: Volume 91, No. 3 (2014)


Natalia Dück$^1$, Karl-Heinz Zimmermann$^2$
$^{1,2}$Hamburg University of Technology
20173, Hamburg, GERMANY

Abstract. Each linear code can be described by a so-called code ideal. In order to utilize this ideal, Gröbner bases are required. Since many results depend on the chosen term order, knowledge of the universal Gröbner basis is advantageous. Singleton codes have the property that the universal Gröbner basis for their code ideals consists of all binomials associated to a codeword whose Hamming weight satisfies the Singleton bound. In this paper, properties of Singleton codes will be established and it will be examined which classical binary linear codes belong to the class of Singleton codes.

Received: May 2, 2013

AMS Subject Classification: 94B05, 94B15

Key Words and Phrases: binary linear code, singleton bound, singleton code, universal Gröbner basis, circuit

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DOI: 10.12732/ijpam.v91i3.1 How to cite this paper?
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 91
Issue: 3