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We confirm a conjecture of Cun Sheng Ding~\cite{Ding-Discrete} claiming thatthe punctured value-sets of a list of eleven trinomials over odd-degreeextensions of the binary field give rise to difference sets with Singerparameters. In the course of confirming the conjecture, we show that thesetrinomials share the remarkable property that every element of the value-set ofeach trinomial has either one or four preimages. We also give a partialresolution of another conjecture of Cun Sheng Ding~\cite{Ding-Discrete}claiming that linear codes constructed from those eleven trinomials aretri-weight.

Difference sets and tri-weight linear codes from trinomials over binary fields