Recently, we published the article:
- From Ideals in Polynomial Rings to Linear Codes Using Groebner Bases, Int. J. Pure Applied Math., vol. 65, no. 1, pp. 41-53, 2010.
This paper studies linear codes as ideals in the group algebra over an elementary abelian
p-group. These codes are described in terms of Groebner bases and corresponding encoding and decoding procedures are given. It is shown 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.
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