Meidl, Wilfried
(2024)
*Generalized bent functions with large dimension.*
Advances in Mathematics of Communications, 18
(5).
pp. 1514-1530.
ISSN 1930-5346 (Print) 1930-5338 (Online)

Official URL: https://dx.doi.org/10.3934/amc.2023004

## Abstract

By a fundamental result by Mesnager et al. in 2018, a generalized bent function (originally defined as a class of functions from an n-dimensional vector space V(p) n a partition P of V(p) n into a cyclic group), is a bent function g: Vn(p) → Fp with, such that for every function C which is constant on the sets of P, the function g +C is bent. The set of these bent functions forms then an affine space of dimension |P| ≤ pn/2. This characterization of generalized bent functions is much more comprehensive than any earlier description. In this article, we analyse some classes of bent functions under this perspec-tive. As shown earlier, Maiorana-McFarland bent functions permit the largest possible partitions, giving rise to pn/2-dimensional affine bent function spaces. The reason behind is their characterization as the bent functions, which are affine restricted to the n/2-dimensional affine subspaces of a trivial cover of V(p) n. We will show that maximal possible partitions can also be obtained for other classes of (regular) bent functions. Most notably, these classes are de-scribed as bent functions which are affine restricted to non-trivial covers of V(p) n. We investigate (largest) partitions for other types of bent functions, in-cluding weakly regular and non-weakly respectively non-dual bent functions. We round off the article giving partitions for bent functions obtained from bent partitions, which includes the partial spread class, and partitions for Carlet’s class C and D.

Item Type: | Article |
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Uncontrolled Keywords: | (generalized) Maiorana-McFarland; admissible bent function; Bent function; generalized bent function; partition |

Divisions: | Faculty of Engineering and Natural Sciences |

Depositing User: | Wilfried Meidl |

Date Deposited: | 27 Aug 2024 15:05 |

Last Modified: | 27 Aug 2024 15:05 |

URI: | https://research.sabanciuniv.edu/id/eprint/49777 |