On metrical properties of the set of self-dual bent functions | Applied Discrete Mathematics. Supplement. 2020. № 13. DOI: 10.17223/2226308X/13/5

On metrical properties of the set of self-dual bent functions

For every bent function / its dual bent function / is uniquely defined. If / = / then / is called self-dual bent and it is called anti-self-dual bent if / = / ф 1. In this work we give a review of metrical properties of the set of self-dual bent functions. We give a complete Hamming distance spectrum between self-dual Maiorana - McFarland bent functions. The set of Boolean functions which are maximally distant from the set of self-dual bent functions is discussed. We give a characterization of automorphim groups of the sets of self-dual and anti-self-dual bent functions in n variables as well as the description of isometric mappings that define bijections between the sets of self-dual and anti-self dual bent functions. The set of isometric mappings which preserve the Rayleigh quotient of a Boolean function is given. As a corollary all isometric mappings which preserve bentness and the Hamming distance between bent function and its dual are given.

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Keywords

булева функция, самодуальная бент-функция, расстояние Хэмминга, изометричное отображение, метрическая регулярность, группа автоморфизмов, отношение Рэлея, Boolean function, self-dual bent function, Hamming distance, isometric mapping, metrical regularity, automorphism group, Rayleigh quotient of Sylvester Hadamard matrix

Authors

Name	Organization	E-mail
Kutsenko A. V.	Novosibirsk National Research State University; S. L. Sobolev Institute of Mathematics SB RAS	AlexandrKutsenko@bk.ru

Всего: 1

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