On affine variety codes from the Klein quartic


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Geil O., ÖZBUDAK F.

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, vol.11, no.2, pp.237-257, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.1007/s12095-018-0285-6
  • Title of Journal : CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
  • Page Numbers: pp.237-257
  • Keywords: Affine variety codes, Grobner basis, Klein curve

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 HOholdt, IEEE Trans. Inform. Theory 46(2), 635-641, 2000 and HOholdt 1998) from Grobner basis theory and for this purpose we develop a new method where we inspired by Buchberger's algorithm perform a series of symbolic computations.