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Piecewise Constructions of Bent and Almost Optimal Boolean Functions

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Abstract

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.

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Authors and Affiliations

  1. INRIA, Domaine de Voluceau, Rocquencourt, University of Paris 8, BP 105, 78153, Cedex, Le Chesnay, France

    Claude Carlet

  2. Department of Mathematics, Southern Illinois University, Carbondale, IL, 62901, USA

    Joseph L. Yucas

Authors
  1. Claude Carlet
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  2. Joseph L. Yucas
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Correspondence to Claude Carlet.

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Communicated by: T. Helleseth

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Carlet, C., Yucas, J.L. Piecewise Constructions of Bent and Almost Optimal Boolean Functions. Des Codes Crypt 37, 449–464 (2005). https://doi.org/10.1007/s10623-005-4036-2

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  • DOI: https://doi.org/10.1007/s10623-005-4036-2

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