On the continuation to bent functions and upper bounds on their number | Applied Discrete Mathematics. Supplement. 2020. № 13. DOI: 10.17223/2226308X/13/4

On the continuation to bent functions and upper bounds on their number

A Boolean bent function / of n variables is a continuation of a Boolean function g of k < n variables if g is a restriction of / to a fixed affine plane of dimension k. We prove that a continuation always exists if k ^ n/2. We obtain an upper bound for the number of continuations. The bound is strengthened in the case k = n - 1, when g is a near-bent function. As a result, we improve the known upper bounds for the number of bent functions. More precisely, we show that for even n ^ 6 there are no more than Cn 2,-²-„,2_+5/2 (^B(ⁿAⁿ - ₂)-f- 1n - 1) + B(n/2 - 1, n - 1)) bent functions of n variables. Here c_n = exp(-1/2 + 23/(18 · 2^n-2))/y^/n and B(d, n) = = 2(II)+(II)+...+(II).

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Keywords

бент-функция, число бент-функций, почти-бент-функция, аффинная плоскость, bent function, number of bent functions, near-bent function, affine plane

Authors

Name	Organization	E-mail
Agievich S. V.	Belarusian State University	agievich@bsu.by

Всего: 1

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