An infinite family of Hadamard matrices of Williamson type
TLDR
A new proof is given of the following theorem of Turyn: Let q = 2 n − 1 be a prime power ≡1 (mod 4); then there exists an Hadamard matrix of order 4 n that is of the Williamson type.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1973-05-01 and is currently open access. It has received 50 citations till now. The article focuses on the topics: Complex Hadamard matrix & Hadamard matrix.read more
Citations
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Hadamard matrices, Sequences, and Block Designs
Jennifer Seberry,Mieko Yamada +1 more
TL;DR: Seberry and Yamada as discussed by the authors considered the problem of finding the maximal determinant of real matrices with entries on the unit disc, and showed that Hadamard matrices satisfy the equality of the following inequality.
Journal ArticleDOI
Some infinite classes of special Williamson matrices and difference sets
TL;DR: There exist Hadamard matrices of special Williamson kind and difference sets of order 4 × 32r × (p1r1···pnrn)4 for any integer n ⩾ 1, primes p1, …, pn, and all nonnegative integers r, r1,…, rn.
Book ChapterDOI
Hadamard matrices, orthogonal designs and construction algorithms
TL;DR: In this paper, the authors discuss algorithms for the construction of Hadamard matrices and give algorithms for constructing orthogonal designs, short amicable and amicable sets for use in the Kharaghani array.
Journal ArticleDOI
Williamson matrices up to order 59
TL;DR: A new algorithm is introduced to search for hard to find Williamson matrices and it turns out that there are none for n = 35, 47, 53, 59 and it seems that the Turyn class may be the only infinite class of these matrices.
References
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Journal ArticleDOI
An infinite class of Williamson matrices
TL;DR: An infinite family is constructed here, and as a corollary it is shown that an Hadamard matrix of order 6( q + 1) exists if q is a prime power ≡ 1 (mod 4).
Journal ArticleDOI
A new construction for Hadamard matrices
L. D. Baumert,Marshall Hall +1 more
TL;DR: In this paper, the Williamson type of Hadamard matrix H is defined as a square matrix of ones and minus ones whose row and column vectors are orthogonal, and it has been conjectured that this condition (n = 1, 2 or At) also insures the existence of an H-matrix.
Journal ArticleDOI
Hadamard matrices of the Williamson type
L. D. Baumert,Marshall Hall +1 more
TL;DR: In this article, it has been conjectured that this condition (n = 1, 2 or 4i) also insures the existence of an Hadamard matrix of that order.