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Quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices: a coding-theoretic approach. (English) Zbl 1440.05051

Summary: 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 coding-theoretic approach, we provide upper bounds on the number of mutually quasi-unbiased Hadamard matrices. We give classifications of a certain class of self-complementary 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.

MSC:

05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
94B25 Combinatorial codes
94B65 Bounds on codes
05E30 Association schemes, strongly regular graphs

Software:

Cliquer; Magma; Hadamard
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Full Text: DOI arXiv

References:

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