Self-dual Hadamard bent sequences
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by
Minjia Shi, Yaya Li, Wei Cheng, Dean Crnković, Denis Krotov, Patrick Solé
2022
Abstract
A new notion of bent sequence related to Hadamard matrices was introduced
recently, motivated by a security application ( Solé et al, 2021). We study
the self dual class in length at most 196. We use three competing methods of
generation: Exhaustion, Linear Algebra and Groebner bases. Regular Hadamard
matrices and Bush-type Hadamard matrices provide many examples. We conjecture
that if v is an even perfect square, a self-dual bent sequence of length v
always exist. We introduce the strong automorphism group of Hadamard matrices,
which acts on their associated self-dual bent sequences. We give an efficient
algorithm to compute that group.
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