An infinite class of supplementary difference sets and Williamson matrices

@article{Xia1991AnIC,
  title={An infinite class of supplementary difference sets and Williamson matrices},
  author={Ming-Yuan Xia and Gang Liu},
  journal={J. Comb. Theory, Ser. A},
  year={1991},
  volume={58},
  pages={310-317}
}
Abstract In this paper we prove that there exist 4-{v; 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 for t ϵ S = {2k + 1:0 ⩽ k ⩽ 16} ∪ {37, 59, 61, 67 } ∪ {2i · 10j · 26k +1: i, j, k ⩾0}. 
SOME NEW FAMILIES OF SDSS AND HADAMARD MATRICES
Abstract In this paper we prove that for any prime power q ≡ 3 (mod 8) there exist 4 – {q2; k, k, k, k; λ} supplementary difference sets (SDSs) with k = q(q – 1)/2, λ = 4k – q2, and Hadamard matricesExpand
A new family of supplementary difference sets and Hadamard matrices
Abstract In this paper we prove that there exist 4-{ν, κ, κ, κ, κ; λ} supplementary difference sets with ν = q2, q ≡ 3(mod 8) a prime power, k = q(q − 1) 2 , λ = 4κ − ν, and Hadamard matrices ofExpand
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First we give an overview of the known supplementary difference sets (SDS) (A_i), i=1..4, with parameters (n;k_i;d), where k_i=|A_i| and each A_i is either symmetric or skew and k_1 + ... + k_4 = n +Expand
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References

SHOWING 1-5 OF 5 REFERENCES
Some Infinite Classes of Hadamard Matrices
TLDR
It is proved that in each case referred to, the same stated condition or conditions, which according to either of the authors give rise to one Hadamard matrix, actually imply the existence of an infinite series of hadamard matrices. Expand
Hadamard Matrices, Baumert-Hall Units, Four-Symbol Sequences, Pulse Compression, and Surface Wave Encodings
  • R. Turyn
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1974
TLDR
A number of special Baumert-Hall sets of units, including an infinite class, are constructed here; these give the densest known classes of Hadamard matrices. Expand
A Hadamard matrix of order 268
TLDR
The existence of Hadamard matrices of order 268 is established and the existence of Baumert-Hall arrays of order 335, and 603 is established as well. Expand
ANTI SYMMETRIC SYSTEM OF SECOND ORDER EVOLUTION EQUATIONS
Abstract Under some conditions to find the interaction of waves is, in the final analysis, to solve kind of anti-symmetric system of second order evolution equations. Thus, In §2 of this paper weExpand
Combinatorial Theory,
  • 1969