| [176897] |
| Title: Gröbner bases for perfect binary codes. |
| Written by: Natalia Dück and Karl-Heinz Zimmermann |
| in: <em>International Journal of Pure and Applied Mathematics (IJPAM)</em>. February (2014). |
| Volume: <strong>91</strong>. Number: (2), |
| on pages: 155-167 |
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| Publisher: AP: |
| Series: 20140225-dueck-ijpam.pdf |
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| ISBN: 10.12732/ijpam.v91i2.2 |
| how published: 14-85 DuZi14b IJPAM |
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Note: khzimmermann, AEG
Abstract: There is a deep connection between linear codes and combinatorial designs. Combinatorial designs can give rise to linear codes and vice versa. In particular, perfect codes always hold combinatorial designs. Recently, linear codes have been associated to binomial ideals by the so-called code ideal which completely describes the code. It will be shown that for a perfect binary linear code, the codewords of minimum Hamming weight are in one-to-one correspondence with the elements of a reduced Gröbner basis for the code ideal with respect to any graded order.