Characterisation and enumeration of a class of semi bent quadratic Boolean functions

Date

2015-01-01

Author

KOÇAK, Neşe
Koçak, Onur Ozan
Özbudak, Ferruh
SAYGI, ZÜLFÜKAR

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In this paper, we consider semi-bentness of quadratic Boolean functions defined for even n and give the characterisation of these functions. Up to our knowledge, semi-bentness of this class has not been investigated before and we proved that semi-bent functions of this form exist only for 6|n. Furthermore, we present a method for enumeration of semi-bent and bent functions in certain classes. Using this method we find the exact number of semi-bent functions of this form. Moreover, we complete some previous partial and incomplete enumeration results for three other classes of semi-bent/bent functions in the literature using this method. We also correct some results on quadratic bent functions stated in Ma et al. (2005).

Subject Keywords

Quadratic boolean functions, Semi-bent functions, Self-reciprocal polynomials, Enumeration, Bent functions

URI

https://hdl.handle.net/11511/42238

Journal

International Journal of Information and Coding Theory

DOI

https://doi.org/10.1504/ijicot.2015.068696

Collections

Department of Mathematics, Article

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Citation Formats

N. KOÇAK, O. O. Koçak, F. Özbudak, and Z. SAYGI, “Characterisation and enumeration of a class of semi bent quadratic Boolean functions,” International Journal of Information and Coding Theory, pp. 39–57, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42238.