  We describe a method of encoding various types of link diagrams, including
those with classical, flat, rigid, welded, and virtual crossings. We show that
this method may be used to encode link diagrams, up to equivalence, in a
notation whose length is a cubic function of the number of 'riser marks'. For
classical knots, the minimal number of such marks is twice the bridge index,
and a classical knot diagram in minimal bridge form with bridge index $b$ may
be encoded in space $\mathcal{O}(b^2)$. A set of moves on the notation is
defined. As a demonstration of the utility of the notation we give another
proof that the Kishino virtual knot is non-classical.
