有限域上函数的非线性

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI:10.1515/dma-2023-0021

V. G. Ryabov

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引用次数: 0

摘要

摘要将函数的非线性和可加性非线性分别定义为到所有仿射映射集合的Hamming距离和到具有非平凡可加转换的所有映射集合的Hamming距离。在揭示非线性与函数特征的傅里叶系数关系的基础上，找到了在任意有限域上实用的重要函数类的非线性评价的方便公式。在偶特征场的情况下，自相关系数的可加性非线性得到了类似的结果。所得到的公式可以表示具有极大可能和高度非线性和可加非线性的特定函数类。

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Nonlinearity of functions over finite fields

Abstract The nonlinearity and additive nonlinearity of a function are defined as the Hamming distances, respectively, to the set of all affine mappings and to the set of all mappings having nontrivial additive translators. On the basis of the revealed relation between the nonlinearities and the Fourier coefficients of the characters of a function, convenient formulas for nonlinearity evaluation for practically important classes of functions over an arbitrary finite field are found. In the case of a field of even characteristic, similar results were obtained for the additive nonlinearity in terms of the autocorrelation coefficients. The formulas obtained made it possible to present specific classes of functions with maximal possible and high nonlinearity and additive nonlinearity.

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来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.