仿射类似物逼近q值逻辑函数对线性流形的限制

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2021-12-01 DOI:10.1515/dma-2021-0037

V. G. Ryabov

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引用次数: 4

摘要

摘要对于有限q元域Fq，建立了表征q值逻辑函数仿射逼近测度的参数与其约束线性流形的类似参数之间的关系。对于q > 2，证明了关于这些参数的Parseval恒等式的一个类比，得到了n位q值逻辑函数的非线性及其对r维流形的限制的有意义的上估计qn−1(q−1)−qn/2−1和qr−1(q−1)−qr/2−1。得到了表征固定维流形上非线性分布的估计。

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Approximation of restrictions of q-valued logic functions to linear manifolds by affine analogues

Abstract For a finite q-element field Fq, we established a relation between parameters characterizing the measure of affine approximation of a q-valued logic function and similar parameters for its restrictions to linear manifolds. For q > 2, an analogue of the Parseval identity with respect to these parameters is proved, which implies the meaningful upper estimates qn−1(q − 1) − qn/2−1 and qr−1(q − 1) − qr/2−1, for the nonlinearity of an n-place q-valued logic function and of its restrictions to manifolds of dimension r. Estimates characterizing the distribution of nonlinearity on manifolds of fixed dimension are obtained.

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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.