An asymptotic lower bound on the number of bent functions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866914991145222144 |
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| author | Potapov, V. N. Taranenko, A. A. Tarannikov, Yu. V. |
| author_facet | Potapov, V. N. Taranenko, A. A. Tarannikov, Yu. V. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_00232 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | An asymptotic lower bound on the number of bent functions Potapov, V. N. Taranenko, A. A. Tarannikov, Yu. V. Combinatorics 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. |
| title | An asymptotic lower bound on the number of bent functions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2108.00232 |