An asymptotic lower bound on the number of bent functionsстатья
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Дата последнего поиска статьи во внешних источниках: 10 июля 2024 г.
Аннотация:A Boolean function f on n variables is said to be a bent function if the absolute value of all its Walsh coefficients is 2^{n/2}. Our main result is a new asymptotic lower bound on the number of Boolean bent functions. It is based on a modification of the Maiorana–McFarland family of bent functions and recent progress in the estimation of the number of transversals in latin squares and hypercubes. By-products of our proofs are the asymptotics of the logarithm of the numbers of partitions of the Boolean hypercube into 2-dimensional affine and linear subspaces.