| [176898] |
| Title: Singleton codes. |
| Written by: Natalia Dück and Karl-Heinz Zimmermann |
| in: <em>International Journal of Pure and Applied Mathematics (IJPAM)</em>. January (2014). |
| Volume: <strong>91</strong>. Number: (3), |
| on pages: 273-290 |
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| Publisher: AP: |
| Series: 201401-dueck-ijpam.pdf |
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| ISBN: 10.12732/ijpam.v91i3.1 |
| how published: 14-95 DuZi14a IJPAM |
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Note: khzimmermann, AEG
Abstract: Each linear code can be described by a so-called code ideal. In order to utilize this ideal, Gröbner bases are required. Since many results depend on the chosen term order, knowledge of the universal Gröbner basis is advantageous. Singleton codes have the property that the universal Gröbner basis for their code ideals consists of all binomials associated to a codeword whose Hamming weight satisfies the Singleton bound. In this paper, properties of Singleton codes will be established and it will be examined which classical binary linear codes belong to the class of Singleton codes.