Asymptotic bounds on the numbers of certain bent functions

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Potapov, Vladimir N. and Özbudak, Ferruh (2024) Asymptotic bounds on the numbers of certain bent functions. Cryptography and Communications . ISSN 1936-2447 (Print) 1936-2455 (Online) Published Online First https://dx.doi.org/10.1007/s12095-024-00726-x

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Abstract

Using recent results of Keevash et al. [10] and Eberhard et al. [8] together with further new detailed techniques in combinatorics, we present constructions of two concrete families of generalized Maiorana-McFarland bent functions. Our constructions improve the lower bounds on the number of bent functions in n variables over a finite field Fp if p is odd and n is odd in the limit as n tends to infinity. Moreover we obtain the asymptotically exact number of two dimensional vectorial Maiorana-McFarland bent functions in n variables over F2 as n tends to infinity.
Item Type: Article
Uncontrolled Keywords: Bent function; Generalized Maiorana-McFarland bent function; Subspace design; Transversal
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Ferruh Özbudak
Date Deposited: 29 Aug 2024 14:39
Last Modified: 29 Aug 2024 14:39
URI: https://research.sabanciuniv.edu/id/eprint/49737

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