Generalized relative difference sets

Abstract

Abstract.A Bruck-Ryser type nonexistence theorem is given for a class of generalized relative difference sets. Some well-known results on (v, k, X)-designs are generalized and a new class of relative difference sets is given.1. A Bruck-Ryser type nonexistence theorem. Let m and n be positive integers with m>l.Let P0 be the identity matrix Imn of order mn; Pi the matrix Jmn of order mn each entry of which is 1; P2 the direct sum of /" taken m times, where J" is the matrix of order n each entry of which is 1. Then P0, Pj, and P2 form a basis for a commutative, linear associative algebra A* over the rationals Q.Let B = Ei-o CiPi, where CiEQ-Then put