On affine variety codes from the Klein quartic

Hans Olav Geil, Ferruh Ozbudak

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3 Citations (Scopus)


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.
Original languageEnglish
JournalCryptography and Communications
Issue number2
Pages (from-to)237-257
Number of pages21
Publication statusPublished - 15 Mar 2019


  • Affine variety codes
  • Gröbner basis
  • Klein curve


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