Constructions of Semi-regular Relative Difference Sets,

J. A. Davis, J. Jedwab, and M. Mowbray (1998, Des. Codes Cryptogr.13, 131–146) gave two new constructions for semi-regular relative difference sets (RDSs). They asked if the two constructions could be unified. In this paper, we show that the two constructions are closely related. In fact, the second construction should be viewed as an extension of the first. Furthermore, we generalize the second construction to obtain new RDSs.