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Towards the classification of self-dual bent functions in eight variables

Abstract

In this paper, we classify quadratic and cubic self-dual bent functions in eight variables with the help of computers. There are exactly four and 45 non-equivalent self-dual bent functions of degree two and three, respectively. This result is achieved by enumerating all eigenvectors with ± 1 entries of the Sylvester Hadamard matrix with an integer programming algorithm based on lattice basis reduction. The search space has been reduced by breaking the symmetry of the problem with the help of additional constraints. The final number of non-isomorphic self-dual bent functions has been determined by exploiting that EA-equivalence of Boolean functions is related to the equivalence of linear codes.

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Correspondence to Alfred Wassermann.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Finite Geometries”

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Feulner, T., Sok, L., Solé, P. et al. Towards the classification of self-dual bent functions in eight variables. Des. Codes Cryptogr. 68, 395–406 (2013). https://doi.org/10.1007/s10623-012-9740-0

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Keywords

  • Boolean functions
  • Bent functions
  • Integer programming
  • EA-equivalence

Mathematics Subject Classification (2000)

  • 06E30
  • 65T50
  • 94A60