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 for complex matrices, and study self-dual class in length at most 90. We use three competing methods generation: Brute force, Linear Algebra Groebner bases. Regular Bush-type provide many examples. strong automorphis...

In this paper, complex singular Wishart matrices and their applications are investigated. In particular, a volume element on the space of positive semidefinite m×m complex matrices of rank n < m is introduced and some transformation properties are established. The Jacobian for the change of variables in the singular value decomposition of general m × n complex matrices is derived. Then the dens...

In this note we utilize a non-trivial block approach due to M. Petrescu to exhibit a Butson-type complex Hadamard matrix of order 19, composed of sixth roots of unity. 1 A new Butson-type complex Hadamard matrix A complex Hadamard matrix H is an n × n complex matrix with unimodular entries such that HH∗ = nIn, where ∗ denotes the Hermitian adjoint and In is the identity matrix of order n. Throu...

Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling of Abelian groups and constructions of complex Hadamard matrices. First, we recover a recent very general construction of complex Hadamard matrices due to Dita [2] via a natural tiling construction. Then we find so...