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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)

- Tao Feng, Weisheng Qiu
- 2007

As pointed out in [23] and [15], constructing optimal codebooks with minimal I max is very difficult in general. This problem is equivalent to line packing in Grassmannian space [6]. In frame theory, such a code-book with Imax minimized is referred to as a Grassmannian frame [20]. The optimal codebooks presented in this paper and the constructions should… (More)

- Xiwang Cao, Weisheng Qiu, Cuie Tang
- 2003

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)

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