(Not) weakly regular univariate bent functions

2013/10/30 by Ayça Çeşmelioğlu, Wilfried Meidl, Çeşmelioğlu, Ayça +1
Computer Science · Medicine · #Cancer Mechanisms and Therapy #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Peptidase Inhibition and Analysis

paper · pdf · doi:10.48550/arxiv.1310.8071

openalex publication_date 2013/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article a procedure to construct bent functions from \F_pⁿ to \F_p by merging plateaued functions which are bent on (n-2)-dimensional subspaces of \F_pⁿ is presented. Taking advantage of such classes of plateaued functions with a simple representation as monomials and binomials, we obtain infinite classes of bent functions with a fairly simple representation. In particular we present the first direct construction of univariate not weakly regular bent functions, and give one class explicitly in a simple representation with binomials.

Citations

• Partially-bent functions

Related

• A Construction of Weakly and Non-Weakly Regular Bent Functions
• New infinite families of p-ary weakly regular bent functions
• Several classes of bent, near-bent and 2-plateaued functions over finite fields of odd characteristic
• Secondary constructions of vectorial p-ary weakly regular bent functions
• There are infinitely many bent functions for which the dual is not bent