Designs, Codes and Cryptography

, Volume 37, Issue 3, pp 449–464 | Cite as

Piecewise Constructions of Bent and Almost Optimal Boolean Functions

  • Claude Carlet
  • Joseph L. Yucas


The first aim of this work was to generalize the techniques used in MacWilliams’ and Sloane’s presentation of the Kerdock code and develop a theory of piecewise quadratic Boolean functions. This generalization led us to construct large families of potentially new bent and almost optimal functions from quadratic forms in this piecewise fashion. We show how our motivating example, the Kerdock code, fits into this setting. These constructions were further generalized to non-quadratic bent functions. The resulting constructions design n-variable bent (resp. almost optimal) functions from n-variable bent or almost optimal functions.


quadratic forms finite fields codes bent functions 

AMS Classification

11T71 94A60 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.INRIA, Domaine de VoluceauRocquencourt, University of Paris 8CedexFrance
  2. 2.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

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