2016/04/10 by Samir Hodžić, Enes Pašalić, Hodžić, S. +1
Computer Science · Engineering · Medicine · #Cancer Mechanisms and Therapy #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1604.02730
openalex publication_date 2016/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Generalized bent (gbent) functions is a class of functions f: ℤ2n → ℤq, where q ≥ 2 is a positive integer, that generalizes a concept of classical bent functions through their co-domain extension. A lot of research has recently been devoted towards derivation of the necessary and sufficient conditions when f is represented as a collection of Boolean functions. Nevertheless, apart from the necessary conditions that these component functions are bent when n is even (respectively semi-bent when n is odd), no general construction method has been proposed yet for n odd case. In this article, based on the use of the well-known Maiorana-McFarland (MM) class of functions, we give an explicit construction method of gbent functions, for any even q >2 when n is even and for any q of the form q=2r (for r>1) when n is odd. Thus, a long-term open problem of providing a general construction method of gbent functions, for odd n, has been solved. The method for odd n employs a large class of disjoint spectra semi-bent functions with certain additional properties which may be useful in other cryptographic applications.