  Using the fact that every worldsheet is ruled by two (light-cone) copies of
worldlines, the recent classification of off-shell supermultiplets of
N-extended worldline supersymmetry is extended to construct standard off-shell
and also unidextrous (on the half-shell) supermultiplets of worldsheet
(p,q)-supersymmetry with no central extension. In the process, a new class of
error-correcting (even-split doubly-even linear block) codes is introduced and
classified for $p+q \leq 8$, providing a graphical method for classification of
such codes and supermultiplets. This also classifies quotients by such codes,
of which many are not tensor products of worldline factors. Also,
supermultiplets that admit a complex structure are found to be depictable by
graphs that have a hallmark twisted reflection symmetry.
