A Unified Approach to Difference Sets with gcd(V,N) > 1

@inproceedings{Davis1999AUA,
  title={A Unified Approach to Difference Sets with gcd(V,N) > 1},
  author={J. Davis and J. Jedwab},
  year={1999}
}
The five known families of difference sets whose parameters (v, k, λ; n) satisfy the condition gcd(v, n) > 1 are the McFarland, Spence, Davis-Jedwab, Hadamard and Chen families. We survey recent work which uses recursive techniques to unify these difference set families, placing particular emphasis on examples. This unified approach has also proved useful for studying semi-regular relative difference sets and for constructing new symmetric designs. 
Packings of partial difference sets.
A packing of partial difference sets is a collection of disjoint partial difference sets in a finite group $G$. This configuration has received considerable attention in design theory, finiteExpand

References

SHOWING 1-10 OF 39 REFERENCES
Some Recent Developments in Difference Sets
difference sets, divisible difference sets, recursive There are five known parameter families for (v, k, λ, n)difference sets satisfying gcd(v, n)>1: the Hadamard, McFarland, Spence, Davis-Jedwab,Expand
Building Symmetric Designs With Building Sets
  • Yury J. Ionin
  • Mathematics, Computer Science
  • Des. Codes Cryptogr.
  • 1999
We introduce a uniform technique for constructing a family of symmetric designs with parameters (v(qm+1-1)/(q-1), kqm,λqm), where m is any positive integer, (v, k, λ) are parameters of an abelianExpand
New Constructions of Menon Difference Sets
TLDR
This paper provides a construction of difference sets in higher exponent groups, and this provides new examples of perfect binary arrays. Expand
New Families of Semi-Regular Relative Difference Sets
We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2. No such RDSs wereExpand
A New Family of Relative Difference Sets in 2-Groups
We recursively construct a new family of ( 26d+4, 8, 26d+4, 26d+1) semi-regular relative difference sets in abelian groups G relative to an elementary abelian subgroup U. The initial case d = 0 ofExpand
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
Constructions of Partial Difference Sets and Relative Difference Sets Using Galois Rings II
TLDR
This paper generalizes and improves the construction of partial difference sets in Des. Expand
A Sharp Exponent Bound for McFarland Difference Sets withp=2
We show that under the self-conjugacy condition a McFarland difference set withp=2 andf?2 in an abelian groupGcan only exist, if the exponent of the Sylow 2-subgroup does not exceed 4. The methodExpand
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 a Family of Covering Extended Building Sets
  • Y. Chen
  • Mathematics, Computer Science
  • Des. Codes Cryptogr.
  • 1999
TLDR
A family of covering extended building sets similar to the ones corresponding to Hadamard difference sets and Spence difference sets are considered and some numerical restrictions on the parameters are derived. Expand
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