Characterization of Linear Structures

  • Authors:
  • Sylvie Dubuc

  • Affiliations:
  • GREYC Département informatique, Université de Caen, 14032 Caen cedex, FRANCE

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2001

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Abstract

We study the notionof linear structure of a function defined from \F^mto \F^n, and in particular of a Boolean function.We characterize the existence of linear structures by means ofthe Fourier transform of the function. For Boolean functions,this characterization can be stated in a simpler way. Finally,we give some constructions of resilient Boolean functions whichhave no linear structure.