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Upper bounds on the numbers of binary plateaued and bent functions

Vladimir N. Potapov

Abstract

The logarithm of the number of binary n-variable bent functions is asymptotically less than $11(2^n)/32$ as n tends to infinity. Keywords: boolean function, Walsh--Hadamard transform, plateaued function, bent function, upper bound

Upper bounds on the numbers of binary plateaued and bent functions

Abstract

The logarithm of the number of binary n-variable bent functions is asymptotically less than as n tends to infinity. Keywords: boolean function, Walsh--Hadamard transform, plateaued function, bent function, upper bound
Paper Structure (5 sections, 17 theorems, 20 equations)

This paper contains 5 sections, 17 theorems, 20 equations.

Table of Contents

  1. Introduction
  2. Fourier transform
  3. Möbius transform
  4. Subspace distribution
  5. Main results

Key Result

Proposition 1

For every $s$-plateaued function, a part of nonzero values of its Walsh--Hadamard transform is equal to $\frac{1}{2^s}$.

Theorems & Definitions (26)

  • Proposition 1
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Lemma 1
  • proof
  • Lemma 2: Carlet, Theorem 2
  • Corollary 1: Carlet, Proposition 96
  • Proposition 4
  • ...and 16 more