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Designs, Codes and Cryptography

, Volume 78, Issue 1, pp 5–50 | Cite as

Four decades of research on bent functions

  • Claude CarletEmail author
  • Sihem Mesnager
Article

Abstract

In this survey, we revisit the Rothaus paper and the chapter of Dillon’s thesis dedicated to bent functions, and we describe the main results obtained on these functions during these last 40 years. We also cover more briefly super-classes of Boolean functions, vectorial bent functions and bent functions in odd characteristic.

Keywords

Boolean functions Bent and p-ary bent functions Plateaued functions Vectorial bent functions Spreads Maiorana-McFarland class 

Mathematics Subject Classification

06E30 94A60 

Notes

Acknowledgments

We thank John Dillon for his kind recollections and detailed information on the early days of bent functions and Bill Kantor for useful information on designs.

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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.LAGA, Department of Mathematics, UMR 7539, CNRSUniversities of Paris 8 and Paris 13Saint-Denis Cedex 02France

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