Hadamard Matrices and Their Applications
A. S. Hedayat,W. D. Wallis +1 more
TLDR
Hadamard matrices have been widely studied in the literature and many of their applications can be found in this paper, e.g., incomplete block designs, Youden designs, orthogonal $F$-square designs, optimal saturated resolution III (SRSIII), optimal weighing designs, maximal sets of pairwise independent random variables with uniform measure, error correcting and detecting codes, Walsh functions, and other mathematical and statistical objects.Abstract:
An $n \times n$ matrix $H$ with all its entries $+1$ and $-1$ is Hadamard if $HH' = nI$. It is well known that $n$ must be 1, 2 or a multiple of 4 for such a matrix to exist, but is not known whether Hadamard matrices exist for every $n$ which is a multiple of 4. The smallest order for which a Hadamard matrix has not been constructed is (as of 1977) 268. Research in the area of Hadamard matrices and their applications has steadily and rapidly grown, especially during the last three decades. These matrices can be transformed to produce incomplete block designs, $t$-designs, Youden designs, orthogonal $F$-square designs, optimal saturated resolution III designs, optimal weighing designs, maximal sets of pairwise independent random variables with uniform measure, error correcting and detecting codes, Walsh functions, and other mathematical and statistical objects. In this paper we survey the existence of Hadamard matrices and many of their applications.read more
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Proceedings ArticleDOI
Some Properties of Hadamard-type Matrices on Finite Fields
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Construction of Orthogonal Main-Effect Plans
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Improved Orthogonal Space-Time Block Codes with Multiple Transmit Antennas Using Hadamard Transform
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Journal ArticleDOI
Some Properties of Binary Matrices and Quasi-Orthogonal Signals Based on Hadamard Equivalence
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TL;DR: The Hadamard equivalence is applied to all the binary matrices of the size m × n and various properties of this equivalence relation and its classes are studied, and the concept of QuasiHadamard matrices (QH matrices) is introduced.