On affine variety codes from the Klein quartic

Olav Geil; Ferruh Ôzbudak

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arXiv · 1706.05688

On affine variety codes from the Klein quartic

Olav Geil·Ferruh Ôzbudak

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Abstract

We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in [12, Ex. 3.2]. Among the codes that we construct almost all have parameters as good as the best known codes according to [9] and in the remaining few cases the parameters are almost as good. To establish the code parameters we apply the footprint bound [10, 7] from Gr\"obner basis theory and for this purpose we develop a new method where we inspired by Buchberger's algorithm perform a series of symbolic computations. 1

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Olav Geil, Ferruh Ôzbudak. 2017-06-18. On affine variety codes from the Klein quartic. https://arxiv.org/abs/1706.05688

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