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
Citations
More filters
Journal ArticleDOI
Anti-Hadamard matrices
Ron Graham,Neil J. A. Sloane +1 more
TL;DR: In this article, it was shown that λ(n), σ(n) are between (2n) −1 ( n 4 ) −n 2 and c√n (2.274)−n, where c is a constant, c ( 2.274 ) n ⩽χ(n)/φ(n/φ 2(n 4 ) n 2, and c (5.172) n/μ(n)-⩽4n 2 (n 4 ).
Journal ArticleDOI
Combining SAT Solvers with Computer Algebra Systems to Verify Combinatorial Conjectures
Edward Zulkoski,Curtis Bright,Albert Heinle,Ilias S. Kotsireas,Krzysztof Czarnecki,Vijay Ganesh +5 more
TL;DR: This paper presents a method and an associated system, called MathCheck, that embeds the functionality of a computer algebra system (CAS) within the inner loop of a conflict-driven clause-learning SAT solver, and leverages the capabilities of several different CAS, namely the SAGE, Maple, and Magma systems.
Journal ArticleDOI
Dynamic Focusing of Large Arrays for Wireless Power Transfer and Beyond
TL;DR: Modular WPT-AD GUs of up to 400 elements utilizing arrays of 65-nm CMOS ICs to focus power on RUs that convert the RF power to dc are demonstrated.
Journal ArticleDOI
A Fast Hadamard Transform for Signals with Sub-linear Sparsity in the Transform Domain
TL;DR: In this article, a new iterative low complexity algorithm for computing the Walsh-Hadamard transform (WHT) of an N-dimensional signal with a K-sparse WHT was presented.
Journal ArticleDOI
A Fast Hadamard Transform for Signals With Sublinear Sparsity in the Transform Domain
TL;DR: A new iterative low-complexity algorithm for computing the Walsh–Hadamard transform (WHT) of an $N$ dimensional signal with a $K$ -sparse WHT based on the subsampling (aliasing) property of the WHT, where a suitable aliasing pattern is induced in the transform domain.