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Related papers: New constructions of quaternary bent functions

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In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…

Classical Analysis and ODEs · Mathematics 2025-08-14 Vyacheslav M. Abramov

Two classes of ternary bent functions of degree four with two and three terms in the univariate representation that belong to the completed Maiorana-McFarland class are found. Binomials are mappings $\F_{3^{4k}}\mapsto\fthree$ given by…

Discrete Mathematics · Computer Science 2025-07-29 Tor Helleseth , Alexander Kholosha , Niki Spithaki

The theory of quaternionic slice regular functions was introduced in 2006 and successfully developed for about a decade over symmetric slice domains, which appeared to be the natural setting for their study. Some recent articles paved the…

Complex Variables · Mathematics 2021-05-04 Graziano Gentili , Caterina Stoppato

In 2017, Zhang et al. proposed a question (not open problem) and two open problems in [IEEE TIT 63 (8): 5336--5349, 2017] about constructing bent functions by using Rothaus' construction. In this note, we prove that the sufficient…

Information Theory · Computer Science 2025-02-17 Fei Guo , Zilong Wang , Guang Gong

Based on a new generalization of Cauchy-Riemann system presented in this paper, we introduce a class of quaternion-valued functions of a quaternionic variable, which are called algebraic regular functions. The set of algebraic regular…

Complex Variables · Mathematics 2015-11-30 Keqin Liu

We consider a new class of quaternionic mappings, associated with the spatial partial differential equations. We describe all mappings from this class using four analytic functions of the complex variable.

Complex Variables · Mathematics 2014-12-17 V. S. Shpakivskyi , T. S. Kuzmenko

In this article a procedure to construct bent functions from $\F_{p^n}$ to $\F_p$ by merging plateaued functions which are bent on ($n-2$)-dimensional subspaces of $\F_{p^n}$ is presented. Taking advantage of such classes of plateaued…

Number Theory · Mathematics 2013-10-31 Ayça Çeşmelioğlu , Wilfried Meidl

A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class…

Complex Variables · Mathematics 2024-02-14 Michael Parfenov

Bent-negabent functions have many important properties for their application in cryptography since they have the flat absolute spectrum under the both Walsh-Hadamard transform and nega-Hadamard transform. In this paper, we present four new…

Information Theory · Computer Science 2022-09-20 Fei Guo , Zilong Wang , Guang Gong

We introduce a new collection of partially global Galois cohomology classes subsuming both plectic Heegner points and mock plectic invariants. The former are recovered as localizations of plectic Heegner classes, while the latter arise as…

Number Theory · Mathematics 2026-04-14 Michele Fornea

Negabent functions as a class of generalized bent functions have attracted a lot of attention recently due to their applications in cryptography and coding theory. In this paper, we consider the constructions of negabent functions over…

Information Theory · Computer Science 2016-06-30 Gaofei Wu , Nian Li , Yuqing Zhang , Xuefeng Liu

In the present paper, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on 2-parameters weight functions. Such classes englobe the well…

Classical Analysis and ODEs · Mathematics 2017-04-13 Sabrine Arfaoui , Anouar Ben Mabrouk

In this paper, the relation between binomial Niho bent functions discovered by Dobbertin et al. and o-polynomials that give rise to the Subiaco and Adelaide classes of hyperovals is found. This allows to expand the class of bent functions…

Combinatorics · Mathematics 2012-11-27 Tor Helleseth , Alexander Kholosha , Sihem Mesnager

In the present work, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of new monogenic polynomials are provided based on 2-parameters weight functions. Such classes extend the well…

Classical Analysis and ODEs · Mathematics 2017-06-06 Sabrine Arfaoui , Anouar Ben Mabrouk

The article is devoted to holomorphic and meromorphic functions of quaternion and octonion variables. New classes of quasi-conformal and quasi-meromorphic mappings are defined and investigated. Properties of such functions such as their…

Complex Variables · Mathematics 2018-12-18 S. V. Ludkovsky

We call a (q-1)-th Kummer extension of a cyclotomic function field a quasi-cyclotomic function field if it is Galois, but non-abelian, over the rational function field with the constant field of q elements. In this paper, we determine the…

Number Theory · Mathematics 2012-07-10 Min Sha , Linsheng Yin

Bent functions are of great importance in both mathematics and information science. The $\mathcal{P}\mathcal{S}$ class of bent functions was introduced by Dillon in 1974, but functions belonging to this class that can be explicitly…

Combinatorics · Mathematics 2013-08-16 Baofeng Wu

In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent…

Information Theory · Computer Science 2024-03-12 Yanjun Li , Jinjie Gao , Haibin Kan , Jie Peng , Lijing Zheng , Changhui Chen

Dillon-like Boolean functions are known, in the literature, to be those trace polynomial functions from $\mathbb{F}_{2^{2n}}$ to $\mathbb{F}_{2}$, with all the exponents being multiples of $2^n-1$ often called Dillon-like exponents. This…

Discrete Mathematics · Computer Science 2024-11-26 Ziran Tu , Sihem Mesnager , Xiangyong Zeng , Nian Li , Yupeng Jiang , Yanan Deng

Let $\mathbb{F}_{p^{n}}$ be the finite field with $p^n$ elements and $\operatorname{Tr}(\cdot)$ be the trace function from $\mathbb{F}_{p^{n}}$ to $\mathbb{F}_{p}$, where $p$ is a prime and $n$ is an integer. Inspired by the works of…

Information Theory · Computer Science 2021-08-03 Xi Xie , Nian Li , Xiangyong Zeng , Xiaohu Tang , Yao Yao