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

Araya, Makoto; Harada, Masaaki; Suda, Sho

doi:10.1090/mcom/3122

Quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices: A coding-theoretic approach
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by Makoto Araya, Masaaki Harada and Sho Suda;

Math. Comp. 86 (2017), 951-984

DOI: https://doi.org/10.1090/mcom/3122

Published electronically: June 29, 2016

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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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