| [176938] |
| Title: From ideals in polynomial rings to linear codes using Groebner bases. |
| Written by: Mehwish Saleemi and Karl-Heinz Zimmermann |
| in: <em>International Journal of Pure and Applied Mathematics (IJPAM)</em>. December (2010). |
| Volume: <strong>65</strong>. Number: (1), |
| on pages: 41-54 |
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| how published: 10-15 SaZi10d IJPAM |
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Note: khzimmermann, AEG
Abstract: In this paper, we investigate linear codes as ideals in the group algebra over an elementary abelian <em>p</em>-group. We provide a description of these codes in terms of Groebner bases and supply corresponding encoding and decoding procedures. In particular, we study generalizations of primitive Reed-Muller codes, construct their Groebner bases, and give their code parameters. Finally, we show 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.