Geometry, Combinatorial Designs and Related Structures: Difference sets: an update

@inproceedings{Jungnickel1997GeometryCD,
  title={Geometry, Combinatorial Designs and Related Structures: Difference sets: an update},
  author={D. Jungnickel and Bernhard Schmidt},
  year={1997}
}
In the last few years there has been rapid progress in the theory of difference sets. This is a survey of these fascinating new developments. 
Recent progress in algebraic design theory
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  • Computer Science, Mathematics
  • Finite Fields Their Appl.
  • 2005
We survey recent results on difference sets, p-ranks and Smith normal forms of certain set-inclusion matrices and subspace-inclusion matrices.
Difference Sets: An Introduction
We give an introductury treatment of the theory of difference sets focusing on the abelian case. This is meant to facilitate understanding of some other articles in this volume which will provide aExpand
A note on difference sets in dihedral groups
Abstract.It is proved that there are no nontrivial difference sets in dihedral groups of order 4pt, where p is a prime, t > 0 is a positive integer.
Abelian difference sets of order n dividing λ
We show that difference sets satisfying the condition n|λ have a product property which can be exploited to construct more difference sets. Many of the newly discovered difference sets arise inExpand
Cyclotomy, Gauss Sums, Difference Sets and Strongly Regular Cayley Graphs
We survey recent results on constructions of difference sets and strongly regular Cayley graphs by using union of cyclotomic classes of finite fields. Several open problems are raised.
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
Foldings of Difference Sets in Abelian Groups
TLDR
It is shown that under some conditions theexistence of a difference set in G implies the existence of another difference set with the same parameters in G′, where G and G′ are abelian groups of the same order. Expand
Relative difference sets fixed by inversion (ii) - character theoretical approach
TLDR
A new family of relative difference sets with forbidden subgroup Z/4Z is constructed and character theory of abelian groups and Galois rings over Z/ 4Z are used. Expand
Bijections Between Group Rings Preserving Character Sums
TLDR
This work exhibits some, in general nonhomomorphic, bijections between finite groups which preserve the absolute value of character sums. Expand
Relative difference sets fixed by inversion (III) - Cocycle theoretical approach
TLDR
A characterization of a group G which contains a semiregular relative difference set R relative to a central subgroup N containing the commutator subgroup [G,G] of G such that rRr=R for all [email protected]?R. Expand
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TLDR
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