Self-dual bent sequences for complex Hadamard matrices
Résumé
A new notion of bent sequence related to Hadamard matrices was introduced recently, motivated by a security application (Solé et al, 2021). In this paper we introduce the analogous notion for complex Hadamard matrices, and we study the self dual class in length at most 98. We use three competing methods of generation: Brute force, Linear Algebra and Groebner bases. Regular Hadamard matrices and Bush-type Hadamard matrices provide many examples. We introduce the strong automorphism group of complex Hadamard matrices, which acts on their associated self-dual bent sequences. We give an efficient algorithm to compute that group.
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