Bent Rectangles

TL;DR

This paper introduces the concept of bent rectangles, special matrices representing generalized regular bent functions, and explores their properties, transformations, and constructions with applications to Boolean functions.

Contribution

It presents new biaffine and bilinear constructions of bent rectangles and studies their partitions, advancing the understanding of generalized bent functions.

Findings

Defined affine transformations of bent rectangles

Proposed new biaffine and bilinear constructions

Illustrated concepts with Boolean case examples

Abstract

We study generalized regular bent functions using a representation by bent rectangles, that is, special matrices with restrictions on rows and columns. We describe affine transformations of bent rectangles, propose new biaffine and bilinear constructions, study partitions of a vector space into affine planes of the same dimension and use such partitions to build bent rectangles. We illustrate the concept of bent rectangles by examples for the Boolean case.