Difference systems of sets and cyclotomy

Difference systems of sets (DSS) are combinatorial configurations that arise in connection with code synchronization. A method for the construction of DSS from partitions of cyclic difference sets was introduced in [V.D. Tonchev, Difference systems of sets and code synchronization, Rend. Sem. Mat. Messina, Ser. II, t. XXV 9 (2003) 217–226] and applied to cyclic difference sets (n,(n-1)/2,(n-3)/4)(n,(n-1)/2,(n-3)/4) of Paley type, where n≡3(mod4) is a prime number. This paper develops similar constructions for prime numbers n≡1(mod4) that use partitions of the set of quadratic residues, as well as more general cyclotomic classes.