• Publications
  • Influence
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
  • 1 November 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
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
Optimal designs, supplementary difference sets and multipliers
Abstract We investigate multipliers of 2 - {v; q2, q2; λ} supplementary difference sets where cyclotomy has been used to construct D-optimal designs.
An infinite family of Goethals-Seidel arrays
TLDR
An infinite family of Goethals-Seidel arrays is constructed and the theorem that if q = 4n - 1 is a prime power ≡ 3 (mod 8), then there exists an Hadamard matrix of order 4n of Goetsch type is proved. Expand
A New Method for Constructing Williamson Matrices
For every prime power q ≡ 1 (mod 4) we prove the existence of (q; x, y)-partitions of GF(q) with q=x2+4y2 for some x, y, which are very useful for constructing SDS, DS and Hadamard matrices. WeExpand
A special class of T-matrices
TLDR
This paper finds T -matrices of the special kind of order t for t = 3, 5, 7, 9, 11, 13, 15, which can be used to generate a large family of T-matrices. Expand
A family of C-partitions and T-matrices
In this article we give the definition of C-partitions in an abelian group, consider the relation between C-partitions, supplementary difference sets and T-matrices, and for an abelian group of orderExpand
Hadamard matrices constructed from supplementary difference sets in the class ℋ1
In this article we give the definition of the class ℋ1 and prove: (1) ℋ1(v) ≠ ϕ for v ∈ = 1 ∪ 2 ∪ 3 where (2) there exists 2 − {2q2; q2 ± q, q2;q2 ± q}Expand
...
1
2
3
...