A Family of Difference Sets in Non-cyclic Groups

Abstract A construction is given for difference sets in certain non-cyclic groups with the parameters v = q s+1 {[ (q s+1 − 1) (q − 1) ] + 1} , k = q s (q s+1 − 1) (q − 1) , λ = q s (q s − 1) (q − 1) , n = q 2 s for every prime power q and every positive integer s . If q s is odd, the construction yields at least 1 2 (q s + 1) inequivalent difference sets in the same group. For q = 5, s = 2 a difference set is obtained with the parameters ( v , k , λ , n ) = (4000, 775, 150, 625), which has minus one as a multiplier.