Isometric mappings of the set of all boolean functions into itself which preserve self-duality and the rayleigh quotient | Applied Discrete Mathematics. Supplement. 2019. № 12. DOI: 10.17223/2226308X/12/16

Isometric mappings of the set of all boolean functions into itself which preserve self-duality and the rayleigh quotient

In the paper, we study isometric mappings of the set of all Boolean functions in n variables into itself which preserve self-duality and the Rayleigh quotient of Boolean function and generalize known results. It is proved that isometric mapping preserves self-duality if and only if it preserves anti-self-duality. The complete characterization of these mappings is obtained. Based on this result, the set of isometric mappings which preserve the Rayleigh quotient of a Boolean function is described. 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, изометричное отображение, самодуальная бент-функция, отношение Рэлея, Boolean function, isometric mapping, self-dual bent function, Rayleigh quotient

Authors

Name	Organization	E-mail
Kutsenko A. V.	Novosibirsk State University	AlexandrKutsenko@bk.ru

Всего: 1

References

Janusz G. J. Parametrization of self-dual codes by orthogonal matrices // Finite Fields Appl. 2007. No. 13(3). P. 450-491.

Rothaus O. On bent functions // J. Combin. Theory. Ser. A. 1976. No. 20(3). P. 300-305).

Hou X.-D. Classification of self dual quadratic bent functions // Des. Codes Cryptogr. 2012. No. 63 (2). P. 183-198.

Carlet C., Danielson L. E., Parker M. G., and Sole P. Self dual bent functions // Int. J. Inform. Coding Theory. 2010. No. 1. P. 384-399.

Feulner T., SokL., Sole P., and Wassermann A. Towards the classification of self-dual bent functions in eight variables // Des. Codes Cryptogr. 2013. No. 68(1). P. 395-406.

Куценко А. В. Спектр расстояний Хэмминга между самодуальными бент-функциями из класса Мэйорана - МакФарланда // Дискретный анализ и исследование операций. 2018. Т. 25. №1. C. 98-119.

Danielsen L. E., Parker M. G., and Sole P. The Rayleigh quotient of bent functions // LNCS. 2009. V. 5921. P. 418-432.

Марков А. А. О преобразованиях, не распространяющих искажения // Избранные труды. Т. II. Теория алгорифмов и конструктивная математика, математическая логика, информатика и смежные вопросы. М.: МЦНМО, 2003. С. 70-93.

Tokareva N. N. The group of automorphisms of the set of bent functions // Discr. Math. Appl. 2010. No. 20 (5). P. 655-664.