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Formal self duality
- Source :
- Cryptography and Communications. 13:815-836
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- We study the notion of formal self duality in finite abelian groups. Formal duality in finite abelian groups has been proposed by Cohn, Kumar, Reiher and Schürmann. In this paper we give a precise definition of formally self dual sets and discuss results from the literature in this perspective. Also, we discuss the connection to formally dual codes. We prove that formally self dual sets can be reduced to primitive formally self dual sets similar to a previously known result on general formally dual sets. Furthermore, we describe several properties of formally self dual sets. Also, some new examples of formally self dual sets are presented within this paper. Lastly, we study formally self dual sets of the form $\{(x,F(x)) \ : \ x\in {\mathbb {F}}_{2^{n}}\}$ { ( x , F ( x ) ) : x ∈ F 2 n } where F is a vectorial Boolean function mapping ${\mathbb {F}}_{2^{n}}$ F 2 n to ${\mathbb {F}}_{2^{n}}$ F 2 n .
- Subjects :
- Discrete mathematics
20C15, 20K01
Computer Networks and Communications
Applied Mathematics
010102 general mathematics
Duality (mathematics)
0102 computer and information sciences
01 natural sciences
Dual (category theory)
Computational Theory and Mathematics
010201 computation theory & mathematics
FOS: Mathematics
Mathematics - Combinatorics
Combinatorics (math.CO)
0101 mathematics
Abelian group
Connection (algebraic framework)
Boolean function
Mathematics
Subjects
Details
- ISSN :
- 19362455 and 19362447
- Volume :
- 13
- Database :
- OpenAIRE
- Journal :
- Cryptography and Communications
- Accession number :
- edsair.doi.dedup.....927a7ac7c37e26eaf55e20ec443b2389