Quasi-unbiased hadamard matrices and weakly unbiased hadamard matrices: A coding-theoretic approach

This paper is concerned with quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices, which are generalizations of unbiased Hadamard matrices, equivalently unbiased bases. These matrices are studied from the viewpoint of coding theory. As a consequence of a codingtheoretic approach, we provide upper bounds on the number of mutually quasiunbiased Hadamard matrices. We give classifications of a certain class of selfcomplementary codes for modest lengths. These codes give quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices. Some modification of the notion of weakly unbiased Hadamard matrices is also provided.