All self-adjoint extensions of minimal linear relation associated with the
discrete symplectic system are characterized. Especially, for the scalar case
on a finite discrete interval some equivalent forms and the uniqueness of the
given expression are discussed and the Krein--von Neumann extension is
described explicitly. In addition, a limit point criterion for symplectic
systems is established. The result partially generalizes even a classical limit
point criterion for the second order Sturm--Liouville difference equations
