An asymptotic lower bound on the number of bent functions
| Autor: | Potapov, V. N., Taranenko, A. A., Tarannikov, Yu. V. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: v.1: 10 pages v.2: 13 pages; all main results remain the same, but we extend the introduction, add many references, change the title, and make a large number of other small improvements |
| Databáze: | arXiv |
| Externí odkaz: |
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