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arXiv · 1504.01236

Quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices: a coding-theoretic approach

Makoto Araya·Masaaki Harada·Sho Suda
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Abstract

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.

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Makoto Araya, Masaaki Harada, Sho Suda. 2015-04-06. Quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices: a coding-theoretic approach. https://arxiv.org/abs/1504.01236

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