New constructions of Hadamard matrices

@article{Leung2020NewCO,
  title={New constructions of Hadamard matrices},
  author={K. H. Leung and K. Momihara},
  journal={J. Comb. Theory, Ser. A},
  year={2020},
  volume={171}
}
In this paper, we obtain a number of new infinite families of Hadamard matrices. Our constructions are based on four new constructions of difference families with four or eight blocks. By applying the Wallis-Whiteman array or the Kharaghani array to the difference families constructed, we obtain new Hadamard matrices of order $4(uv+1)$ for $u=2$ and $v\in \Phi_1\cup \Phi_2 \cup \Phi_3 \cup \Phi_4$; and for $u\in \{3,5\}$ and $v\in \Phi_1\cup \Phi_2 \cup \Phi_3$. Here, $\Phi_1=\{q^2:q\equiv 1… Expand
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References

SHOWING 1-10 OF 28 REFERENCES
Paley partial difference sets in groups of order n4 and 9n4 for any odd n>1
TLDR
A recursive theorem is given that for all odd n>1 constructs Paley partial difference sets in certain groups of order n^4 and 9n^4. Expand
On the Existence of Abelian Hadamard Difference Sets and a New Family of Difference Sets
We present a construction of Hadamard difference sets in abelian groups of order 4p4n, whose Sylowp-subgroups are elementary. By a standard composition procedure, we can now conclude that (4h2,Expand
On Hadamard matrices
Abstract Recent advances in the construction of Hadamard matrices have depended on the existence of Baumert-Hall arrays and four (1, −1) matrices A, B, C, D of order m which are of Williamson type,Expand
Constructions of Hadamard Difference Sets
TLDR
It is concluded that there exist Hadamard difference sets with parameters (4m2, 2m2? m, m2?m), wherem=2a3b52c1132c2172c3p21p22?p2twitha, b, c1, c2, c3positive integers and where eachpjis a prime congruent to 3 modulo 4, 1?j?t. Expand
A Unifying Construction for Difference Sets
We present a recursive construction for difference sets which unifies the Hadamard, McFarland, and Spence parameter families and deals with all abelian groups known to contain such difference sets.Expand
On the products of Hadamard matrices, Williamson matrices and other orthogonal matrices using M-structures
The new concept of M-structures is used to unify and generalize a number of concepts in Hadamard matrices including Williamson matrices, Goethals-Seidel matrices, Wallis-Whiteman matrices andExpand
ORTHOGONAL MATRICES WITH ZERO DIAGONAL
1. Introduction. C-matrices appear in the literature at various places; for a survey, see [11]. Important for the construction of Hadamard matrices are the symmetric C-matrices, of order v = 2 (modExpand
An infinite class of supplementary difference sets and Williamson matrices
TLDR
It is proved that there exist 4-{v; k,k, k, k; k; λ} supplementary difference sets (SDSs) with v = q2, q ≡ 1 (mod 4) a prime power, k = q(q − 1) 2 , λ = 4k − v, and Williamson matrices of order 4tv are proved. Expand
Some Infinite Classes of Special Williamson Matrices and Difference Sets
  • Ming-Yuan Xia
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • 1992
TLDR
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. Expand
New Hadamard matrices of order 4p2 obtained from Jacobi sums of order 16
TLDR
It is shown that there is a regular Hadamard matrix of order 4p2 provided that p = a ± 2b or p + δ12b + 4 δ2c + 4δ1δ2d with δi = ±1. Expand
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