Some general properties of modified bent functions through addition of indicator functions

Properties of a secondary bent function construction that adds the indicator of an affine subspace of arbitrary dimension to a given bent function in n variables are obtained. Some results regarding normal and weakly normal bent functions are generalized. An upper bound for the number of generated b...

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Bibliographic Details
Published in:Cryptography and communications 2021-11, Vol.13 (6), p.909-926
Main Author: Kolomeec, Nikolay
Format: Article
Language:English
Subjects:
Boolean Functions and Their Applications V
Circuits
Coding and Information Theory
Communications Engineering
Computer Science
Data Structures and Information Theory
Information and Communication
Mathematical analysis
Mathematics of Computing
Networks
Upper bounds
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Summary:Properties of a secondary bent function construction that adds the indicator of an affine subspace of arbitrary dimension to a given bent function in n variables are obtained. Some results regarding normal and weakly normal bent functions are generalized. An upper bound for the number of generated bent functions is proven. This bound is attained if and only if the given bent function is quadratic. In certain cases, the addition of the indicator of an m -dimensional subspace, for different m , will not generate bent functions. Such examples are presented for any even n ≥ 10. It is proven that there exists an infinite family of Maiorana–McFarland bent functions such that the numbers of generated bent functions differ for the bent function and its dual function.
ISSN:1936-2447
1936-2455
DOI:10.1007/s12095-021-00528-5