Generalized constructions of Menon-Hadamard difference sets

New Constructions of Menon Difference Sets

Constructions of Hadamard Difference Sets

Using a spread of PG(3; p) and certain projective two-weight codes, we give a general construction of Hadamard diierence sets in groups H (Z p) 4 , where H is either the Klein 4-group or the cyclic group of order 4, and p is an odd prime. In the case p 3 (mod 4), we use an ovoidal bration of PG(3; p) to construct Hadamard diierence sets, this construction includes Xia's construction of Hadamard...

Cyclotomic constructions of skew Hadamard difference sets

Article history: Received 12 January 2011 Available online xxxx

Two Generalized Constructions of Relative Difference Sets

We give two generalizations of some known constructions of relative difference sets. The first one is a generalization of a construction of RDS by Chen, Ray-Chaudhuri and Xiang using the Galois ring GR(4,m). The second one generalizes a construction of RDS by Ma and Schmidt from the setting of chain rings to a setting of more general rings.

A Summary of Menon Difference Sets