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The group of automorphisms of the set of bent functions

Published/Copyright: January 7, 2011
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Discrete Mathematics and Applications
From the journal Volume 20 Issue 5-6

Abstract

The bent functions are the Boolean functions of an even number of variables which are at the maximum possible distance from the set of all affine functions. In this paper, it is shown that each isometric mapping of the set of Boolean functions of n variables to itself preserving the class of bent functions is a combination of an affine transformation of coordinates and a shift by an affine function. It is proved that the affine functions are precisely all Boolean functions which are at the maximum possible distance from the class of bent functions.

Received: 2010-04-19
Published Online: 2011-01-07
Published in Print: 2010-December

© de Gruyter 2010

Articles in the same Issue

  1. Bounds for the number of Boolean functions admitting affine approximations of a given accuracy
  2. Identification of a binary Markov chain of order s with r partial connections subjected to additive distortions
  3. On conditional Internet graphs whose vertex degrees have no mathematical expectation
  4. An estimate of the probability of localisation of the diameter of a random scale-free graph
  5. On a recursive class of plateaued Boolean functions
  6. On the distribution of some characteristics of a quasimonotone mapping
  7. The expressibility problem in a lattice with closure operation
  8. An algorithm to restore a linear recurring sequence over the ring R = Zpn from a linear complication of its highest coordinate sequence
  9. The uniform id-decomposition of functions of many-valued logic over homogeneous functions
  10. The completeness problem in the function algebra of linear integer-coefficient polynomials
  11. Circuits for disjunction admitting short unitary diagnostic tests
  12. The group of automorphisms of the set of bent functions
  13. Complexity of multiplication in commutative group algebras over fields of prime characteristic
  14. The summation of Markov sequences on a finite abelian group
  15. The asymptotics of the number of repetition-free Boolean functions in the basis B1
https://doi.org/10.1515/dma.2010.040

Articles in the same Issue

  1. Bounds for the number of Boolean functions admitting affine approximations of a given accuracy
  2. Identification of a binary Markov chain of order s with r partial connections subjected to additive distortions
  3. On conditional Internet graphs whose vertex degrees have no mathematical expectation
  4. An estimate of the probability of localisation of the diameter of a random scale-free graph
  5. On a recursive class of plateaued Boolean functions
  6. On the distribution of some characteristics of a quasimonotone mapping
  7. The expressibility problem in a lattice with closure operation
  8. An algorithm to restore a linear recurring sequence over the ring R = Zpn from a linear complication of its highest coordinate sequence
  9. The uniform id-decomposition of functions of many-valued logic over homogeneous functions
  10. The completeness problem in the function algebra of linear integer-coefficient polynomials
  11. Circuits for disjunction admitting short unitary diagnostic tests
  12. The group of automorphisms of the set of bent functions
  13. Complexity of multiplication in commutative group algebras over fields of prime characteristic
  14. The summation of Markov sequences on a finite abelian group
  15. The asymptotics of the number of repetition-free Boolean functions in the basis B1
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