On some properties of self-dual generalized bent functions | Applied Discrete Mathematics. Supplement. 2021. № 14. DOI: 10.17223/2226308X/14/6

On some properties of self-dual generalized bent functions

Bent functions of the form Fn Z_q, where q > 2 is a positive integer, are known as generalized bent (gbent) functions. A gbent function for which it is possible to define a dual gbent function is called regular. A regular gbent function is said to be self-dual if it coincides with its dual. We obtain the necessary and sufficient conditions for the self-duality of gbent functions from Eliseev - Maiorana - McFarland class. We find the complete Lee distance spectrum between all self-dual functions in this class and obtain that the minimal Lee distance between them is equal to q • 2^n-3. For Boolean case, there are no affine bent functions and self-dual bent functions, while it is known that for generalized case affine bent functions exist, in particular, when q is divisible by 4. We prove the non-existence of affine self-dual gbent functions for any natural even q. A new class of isometries preserving self-duality of a gbent function is presented. Based on this, a refined classification of self-dual gbent functions of the form F⁴ Z₄ is given.

Download file

Counter downloads: 25

Keywords

Lee distance, Eliseev - Maiorana - McFarland bent function, generalized bent function, self-dual bent function

Authors

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

Всего: 1

References

Singh B. K. On cross-correlation spectrum of generalized bent functions in generalized Maiorana - McFarland class // Inform. Sci. Lett. 2013. V. 2. No. 3. P. 139-145.

Kutsenko A. V. The Hamming distance spectrum between self-dual Maiorana - McFarland bent functions // J. Appl. Industr. Math. 2018. V. 12. No. 1. P. 112-125.

Sok L., Shi M., and Sole P. Classification and construction of quaternary self-dual bent functions // Cryptogr. Commun. 2018. V. 10. No. 2. P. 277-289.

Hou X.-D. Classification of p-ary self dual quadratic bent functions, p odd // J. Algebra. 2013. V. 391. P. 62-81.

Tokareva N. Bent Functions: Results and Applications to Cryptography. Acad. Press, Elsevier, 2015. 230 p.

Ce§melioglu A., Meidl W., and Pott A. On the dual of (non)-weakly regular bent functions and self-dual bent functions // Adv. Math. Commun. 2013. V. 7. No. 4. P. 425-440.

Токарева Н. Н. Обобщения бент-функций. Обзор работ // Дискрет. анализ исслед. опер. 2010. Т. 17. №1. С. 33-62.

Schmidt K.-U. Quaternary constant-amplitude codes for multicode CDMA // IEEE Trans. Inform. Theory. 2009. V. 55. No. 4. P. 1824-1832.

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