Summary: Let \(\mathbb Q_{2^s}\) be the unique unramifed extension of the two-adic field \(\mathbb Q_2\) of degree \(s\). Let \(R\) be the ring of integers in \(\mathbb Q_{2^s}\). Let \(G\) be a simply connected Chevalley group corresponding to an irreducible simply laced root system. Then the finite group \(G(R/4R)\) has a two-fold central extension \(G'(R/4R)\) constructed by means of the Hilbert symbol on \(\mathbb Q_{2^s}\). In this paper, we construct a natural correspondence between genuine representations of \(G'(R/4R)\) and representations of the Chevalley group \(G(R/2R)\).