  This note presents an encoding and a decoding algorithms for a forest of
(labelled) rooted uniform hypertrees and hypercycles in linear time, by using
as few as $n - 2$ integers in the range $[1,n]$. It is a simple extension of
the classical Pr\"{u}fer code for (labelled) rooted trees to an encoding for
forests of (labelled) rooted uniform hypertrees and hypercycles, which allows
to count them up according to their number of vertices, hyperedges and
hypertrees. In passing, we also find Cayley's formula for the number of
(labelled) rooted trees as well as its generalisation to the number of
hypercycles found by Selivanov in the early 70's.
