IJPAM: Volume 73, No. 4 (2011)
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 . To this end, the extented alphabet 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