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 |
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Pages (from-to) | 951-984 |
Number of pages | 34 |
Journal | Mathematics of Computation |
Volume | 86 |
Issue number | 304 |
DOIs | |
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