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On affine variety codes from the Klein quartic

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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 Kolluru et al., (Appl. Algebra Engrg. Comm. Comput. 10(6):433–464, 2000, Ex. 3.2). Among the codes that we construct almost all have parameters as good as the best known codes according to Grassl (2007) and in the remaining few cases the parameters are almost as good. To establish the code parameters we apply the footprint bound (Geil and Høholdt, IEEE Trans. Inform. Theory 46(2), 635–641, 2000 and Høholdt 1998) from Gröbner basis theory and for this purpose we develop a new method where we inspired by Buchberger’s algorithm perform a series of symbolic computations.

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Acknowledgements

The authors are grateful to Department of Mathematical Sciences, Aalborg University for supporting a one-month visiting professor position for the second listed author.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark

    Olav Geil & Ferruh Özbudak

  2. Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey

    Ferruh Özbudak

Authors
  1. Olav Geil
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  2. Ferruh Özbudak
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Correspondence to Olav Geil.

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This article is part of the Topical Collection on Special Issue on Coding Theory and Applications

Supported from The Danish Council for Independent Research (Grant No. DFF–4002-00367), METU Coordinatorship of Scientific Research Projects via grant for projects BAP-01-01-2016-008 and BAP-07-05-2017-007.

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Geil, O., Özbudak, F. On affine variety codes from the Klein quartic. Cryptogr. Commun. 11, 237–257 (2019). https://doi.org/10.1007/s12095-018-0285-6

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  • DOI: https://doi.org/10.1007/s12095-018-0285-6

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