
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Rings, Modules, and Algebras
