On binary quadratic symmetric bent and almost bent functions

TL;DR

This paper introduces a new simple construction method for binary quadratic symmetric bent and almost bent functions, highlighting their self-dual and anti-self-dual properties for even variables, and their affine equivalence to Maiorana-McFarland type.

Contribution

It provides a novel, simplified construction for certain bent and almost bent functions that are not of the Maiorana-McFarland type but are affine equivalent to it.

Findings

Constructed new classes of symmetric bent functions

Identified self-dual and anti-self-dual properties for even variables

Demonstrated affine equivalence to Maiorana-McFarland functions

Abstract

We give a new simple construction for known binary quadratic symmetric bent and almost bent functions. In particular, for even number of variables, they are self-dual and anti-self-dual quadratic bent functions, respectively, which are not of the Maiorana-McFarland type, but affine equivalent to it.