  Let $F$ be a non-archimedean local field of odd residual characteristic. We
compute the Jordan set of a simple cuspidal representation of a symplectic
group over $F$, using explicit computations of generators of the Hecke algebras
of covers reflecting the parabolic induction under study. When $F$ is a
$p$-adic field we obtain the Langlands parameter of the representation.
