Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Characterization for a generic construction of bent functions and its consequences

Yanjun Li, Jinjie Gao, Haibin Kan, Jie Peng, Lijing Zheng, Changhui Chen

TL;DR

This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent functions.

Abstract

In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent functions.

Characterization for a generic construction of bent functions and its consequences

TL;DR

This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent functions.

Abstract

In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent functions.
Paper Structure (4 sections, 5 theorems, 30 equations)

This paper contains 4 sections, 5 theorems, 30 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. A characterization of a generic construction of bent functions
  4. Conclusion

Key Result

Theorem 1

Li et al.-2021 Let $i$ be an integer with $1\leq i\leq r$, $f,g_i\in\mathcal{B}_n$, and let $\phi=(\phi_1,\phi_2,\ldots,\phi_r)$ be the $(n,r)$-function with $\phi_i=f+g_i$. If the sum of any odd number of functions in $f,g_1,\ldots,g_r$ is a bent function, and its dual is equal to the sum of the du where $\varphi=(\varphi_1,\varphi_2,\ldots,\varphi_r)$ is the $(n,r)$-function with $\varphi_i(x)=f

Theorems & Definitions (12)

  • Definition 1
  • Theorem 1
  • Definition 2: $\mathbf{P_r}$
  • Theorem 2
  • proof
  • Corollary 1
  • proof
  • Corollary 2
  • proof
  • Corollary 3
  • ...and 2 more