Self-dual Hadamard bent sequences

03/30/2022

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by   Minjia Shi, et al.

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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.