TY - JOUR
T1 - Quasi-unbiased hadamard matrices and weakly unbiased hadamard matrices
T2 - A coding-theoretic approach
AU - Araya, Makoto
AU - Harada, Masaaki
AU - Suda, Sho
N1 - Publisher Copyright:
© 2016 American Mathematical Society.
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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U2 - 10.1090/mcom/3122
DO - 10.1090/mcom/3122
M3 - Article
AN - SCOPUS:85008439803
SN - 0025-5718
VL - 86
SP - 951
EP - 984
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 304
ER -