Paley Hadamard Difference Sets and Paley Type Partial Difference Sets

This chapter deals with Paley Hadamard difference sets and Paley type partial difference sets (PDSs). It focuses on Paley core matrices and relative Gauss sums, and the construction of Paley type PDS from a covering extended building set. Davis and Leung and Ma constructed Paley type PDS in p‐groups that are not elementary abelian groups. Polhill gave the construction of Paley type PDSs in groups with the orders which are not a prime power. Weng and Hu constructed Paley Hadamard difference sets from Paley type PDS and skew Hadamard difference sets. Their theorem is a generalization of Stanton and Sprott's work.