Quadratic bent functions and their duals

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-06-14 DOI:10.1007/s00200-022-00564-5

Kanat Abdukhalikov, Rongquan Feng, Duy Ho

引用次数: 0

Abstract

We obtain geometric characterizations of the dual functions for quadratic bent and vectorial bent functions in terms of quadrics. Additionally, using the zeros of the polynomial \(X^{q+1}+X+a\) which have been studied recently in the literature, we provide some examples of binomial quadratic bent functions on \(\mathbb {F}_{q^4}\) and \(\mathbb {F}_{q^6}\), where q is a power of 2.

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二次弯曲函数及其对偶

我们从二次弯曲和矢量弯曲函数的二次函数的几何特征出发，得到了二次弯曲和矢量弯曲函数的几何特征。此外，利用文献中最近研究的多项式 \(X^{q+1}+X+a\) 的零点，我们提供了一些关于 \(\mathbb {F}_{q^4}\) 和 \(\mathbb {F}_{q^6}\) 的二项式二次弯曲函数的例子，其中 q 是 2 的幂。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.