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

Luo, Gaojun; Cao, Xiwang; Mesnager, Sihem

doi:10.1007/s12095-019-00371-9

Cited by 9 publications

(9 citation statements)

References 20 publications

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“…For n = 3, bent functions have the distribution (12,9,6). By experiments we could not find a ternary bent function in three variables with other distribution and, therefore, we conjecture that for odd n, there is a single distribution of function values in the value vectors of bent functions.…”

Section: Ternary Bent Functionsmentioning

confidence: 78%

“…It is important to notice that for n = 3, these basic bent functions, as well as all other bent functions, have the same distribution of function values D 3 = (6,9,12). As in the previous cases for n = 1 and n = 2, all bent functions for n = 3 are split into 6 classes mutually related by encoding of function values.…”

Section: Generalizationsmentioning

confidence: 80%

“…As in the previous cases for n = 1 and n = 2, all bent functions for n = 3 are split into 6 classes mutually related by encoding of function values. The first class consists of functions with the composition (9,12,6) and the representant is the function q 1 = x 1 x 2 ⊕ (x 3 ) 2 . The other classes consist of functions with permuted values of the composition elements.…”

Section: Generalizationsmentioning

confidence: 99%

“…The other classes consist of functions with permuted values of the composition elements. For example, functions with the composition (9,6,12) are a different class, whose representant is q 3 = (x 1 ) 2 ⊕(x 2 ) 2 ⊕(x 3 ) 2 . We define several permutation matrices by referring to matrices describing steps in Cooley-Tukey FFT…”

Section: Generalizationsmentioning

confidence: 99%

See 3 more Smart Citations

Construction of Ternary Bent Functions by FFT-Like Permutation Algorithms

Stanković

Stanković²,

Moraga

et al. 2021

IEICE Trans. Inf. & Syst.

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Binary bent functions have a strictly specified number of non-zero values. In the same way, ternary bent functions satisfy certain requirements on the elements of their value vectors. These requirements can be used to specify six classes of ternary bent functions. Classes are mutually related by encoding of function values. Given a basic ternary bent function, other functions in the same class can be constructed by permutation matrices having a block structure similar to that of the factor matrices appearing in the Good-Thomas decomposition of Cooley-Tukey Fast Fourier transform and related algorithms.

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Section: Ternary Bent Functionsmentioning

confidence: 78%

Section: Generalizationsmentioning

confidence: 80%

Section: Generalizationsmentioning

confidence: 99%

Section: Generalizationsmentioning

confidence: 99%

See 2 more Smart Citations

Construction of Ternary Bent Functions by FFT-Like Permutation Algorithms

Stanković

Stanković²,

Moraga

et al. 2021

IEICE Trans. Inf. & Syst.

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show abstract

“…Next steps for the classification of qubic self-dual bent functions in 8 variables were made in [6], while quadratic self-dual bent functions were completely characterized in [7]. Constructions and properties of self-dual Boolean bent functions were studied in [9,19,23]. The overview of the known metrical properties of self-dual bent functions can be found in [18].…”

Section: Introductionmentioning

confidence: 99%

On some properties of self-dual bent functions

Kutsenko¹

2018

Applied Discrete Mathematics. Supplement

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Bent functions of the form F n 2 → Z q , 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 functions coincide. We give necessary and sufficient conditions for the self-duality of Maiorana-McFarland gbent functions and find Hamming and Lee distances spectrums between them. We find all self-dual gbent functions symmetric with respect to two variables and prove that self-dual gbent function can not be affine. The properties of sign functions of self-dual gbent functions are considered. Symmetries that preserve self-duality are also discussed.The work is supported by Mathematical Center in Akademgorodok under agreement No.

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Metrical properties of self-dual bent functions

Kutsenko

2019

Des. Codes Cryptogr.

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

Cited by 9 publications

References 20 publications

Construction of Ternary Bent Functions by FFT-Like Permutation Algorithms

Construction of Ternary Bent Functions by FFT-Like Permutation Algorithms

On some properties of self-dual bent functions

Metrical properties of self-dual bent functions

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