A generalized Boolean function with flat Walsh - Hadamard spectrum is called generalized bent (gbent) function. Gbent function that coincides with its dual bent function is called self-dual. In this paper, we study isometric mappings of the set of all generalized Boolean functions into itself that preserve self-duality. A new mapping that preserves the self-duality of a gbent function is proposed. We introduce the concept of the action of an unitary operator on the set of generalized Boolean functions in n variables, represented by their characteristic vectors. Within the considered class of unitary operators, all mappings that preserve self-duality are described. A generalized form of isometric mapping corresponding to the complex conjugation of the characteristic vector is investigated.
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- Title Characterization of some classes of isometric mappings that preserve self-duality of generalized bent function
- Headline Characterization of some classes of isometric mappings that preserve self-duality of generalized bent function
- Publesher
Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 69
- Date:
- DOI 10.17223/20710410/69/2
Keywords
generalized Boolean function, self-dual bent finction, isometric mappingAuthors
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Characterization of some classes of isometric mappings that preserve self-duality of generalized bent function | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2025. № 69. DOI: 10.17223/20710410/69/2
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