Recently, we studied linear codes as ideals in the group algebra over an elementary abelian p-group. These codes can be described in terms of Groebner bases which in turn provide encoding and decoding procedures. In particular, we investigated generalizations of primitive Reed-Muller codes and constructed corresponding Groebner bases. We also showed that the class of codes studied contains an interesting family of linear codes. These codes have a designed Hamming distance and turn out to be superior to the primitive Reed-Muller codes in the non-binary case.
AMS Subject Classification: 13P10, 94B05
Keywords: Commutative polynomial rings, ideals, Groebner bases, Reed-Muller codes, decoding.
M. Saleemi, K.-H. Zimmermann: From Ideals in Polynomial Rings to Linear Codes using Groebner Bases. Int. J. Pure Appl. Math., to appear.
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