# On constructions and properties of self-dual generalized bent functions

@inproceedings{Kutsenko2021OnCA, title={On constructions and properties of self-dual generalized bent functions}, author={A. Kutsenko}, year={2021} }

Bent functions of the form F2 → Zq, where q > 2 is a positive integer, are known as generalized bent (gbent) functions. Gbent functions for which it is possible to define a dual gbent function are called regular. A regular gbent function is said to be self-dual if it coincides with its dual. In this paper we explore self-dual gbent functions for even q. We consider several primary and secondary constructions of such functions. It is proved that the numbers of self-dual and anti-self dual gbent… Expand

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SHOWING 1-10 OF 41 REFERENCES

The group of automorphisms of the set of self-dual bent functions

- Mathematics, Physics
- Cryptography and Communications
- 2020

All isometric mappings which preserve bentness and the Hamming distance between bent function and its dual are described and the complete characterization of these mappings is obtained. Expand

Metrical properties of self-dual bent functions

- Computer Science, Mathematics
- Des. Codes Cryptogr.
- 2020

It is proved that within the set of sign functions of self-dual bent functions in n ⩾ 4 variables there exists a basis of the eigenspace of the Sylvester Hadamard matrix attached to the eigenvalue 2 n / 2. Expand

Several new classes of self-dual bent functions derived from involutions

- Mathematics, Computer Science
- Cryptography and Communications
- 2019

This paper proposes a construction of involutions from linear translators, and provides two methods for constructing new involutions by utilizing some given involutions. Expand

Self-dual bent functions

- Computer Science, Mathematics
- Int. J. Inf. Coding Theory
- 2010

All self-dual bent Boolean functions in ≤ 6 variables and all quadratic such functions in eight variables are given, up to a restricted form of affine equivalence. Expand

On the dual of (non)-weakly regular bent functions and self-dual bent functions

- Computer Science, Mathematics
- Adv. Math. Commun.
- 2013

The class of dual-bent functions containing the class of weakly regular bent functions as a proper subclass is defined, and self-duality for bent functions in odd characteristic is analyzed, and quadratic bent functions are characterized. Expand

Complete Characterization of Generalized Bent and 2k-Bent Boolean Functions

- Computer Science, Mathematics
- IEEE Transactions on Information Theory
- 2017

It is proved that Hodžić and Pasalic’s conditions of generalized bent functions are not only sufficient but also necessary, and completely characterize generalizedbent functions in terms of their component functions. Expand

Towards the classification of self-dual bent functions in eight variables

- Mathematics, Computer Science
- Des. Codes Cryptogr.
- 2013

The final number of non-isomorphic self-dual bent functions has been determined by exploiting that EA-equivalence of Boolean functions is related to the equivalence of linear codes. Expand

Parametrization of self-dual codes by orthogonal matrices

- Computer Science, Mathematics
- Finite Fields Their Appl.
- 2007

The subgroups of O"m generated by the permutation matrices and one transvection are determined in the Generator Theorem, which generalizes the known result that a self-dual doubly-even code exists only in lengths divisible by 8. Expand

Generalized Bent Functions and Their Properties

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 1985

The nature of the Fourier coefficients of a bent function is examined and a proof for the non-existence of bent functions over Jqm, m odd, is given for many values of q of the form q = 2 (mod 4). Expand

Construction methods for generalized bent functions

- Mathematics, Computer Science
- Discret. Appl. Math.
- 2018

The long-term open problem of providing a general construction method of gbent functions, for odd $n$, has been solved and the method employs a large class of disjoint spectra semi-bent functions with certain additional properties which may be useful in other cryptographic applications. Expand