Let (K, +, *) be an odd order presemifield with commutative multiplication. We show that the set of nonzero squares of (K, *) is a skew Hadamard difference set or a Paley type partial difference set in (K, +) according as q is congruent to 3 mod-ulo 4 or q is congruent to 1 modulo 4. Applying this result to the Coulter–Matthews presemifield and the… (More)
We give some new methods for constructing perfect arrays. Some results on the liftability of the perfect ternary sequences are obtained. In addition, we present a new perfect ternary array with index group Z/sub 2//sup r/.
Very recently, J.F.Dillon, and H.Dobbertin proved that, the image set of function ∆ k (x) = (x + 1) d + x d + 1, (where d = 2 2k − 2 k + 1), is a new cyclic difference set in the additive group of the finite field GF (2 m). Using Fourier analysis on the additive group, we prove that certain sets, constructed by using Dickson polynomials, form a new cyclic… (More)