A family of difference sets in non-cyclic groups

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Abstract

A construction is given for difference sets in certain non-cyclic groups with the parameters v = qs+1{[(qs+1 − 1)(q − 1)] + 1}, k = qs(qs+1 − 1)(q − 1), λ = qs(qs − 1)(q − 1), n = q2s for every prime power q and every positive integer s. If qs is odd, the construction yields at least 12(qs + 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.

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