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

Makoto Araya; Masaaki Harada; Sho Suda

doi:10.1090/mcom/3122

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

Makoto Araya, Masaaki Harada, Sho Suda

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 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.

Original language	English
Pages (from-to)	951-984
Number of pages	34
Journal	Mathematics of Computation
Volume	86
Issue number	304
DOIs	https://doi.org/10.1090/mcom/3122
Publication status	Published - 2017

Keywords

Selfcomplementary code
Unbiased Hadamard matrix
Unbiased weighing matrix

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/mcom/3122

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T2 - A coding-theoretic approach

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PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Selfcomplementary code

KW - Unbiased Hadamard matrix

KW - Unbiased weighing matrix

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JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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