  LDPC codes constructed from permutation matrices have recently attracted the
interest of many researchers. A crucial point when dealing with such codes is
trying to avoid cycles of short length in the associated Tanner graph, i.e.
obtaining a possibly large girth. In this paper, we provide a framework to
obtain constructions of such codes. We relate criteria for the existence of
cycles of a certain length with some number-theoretic concepts, in particular
with the so-called Sidon sets. In this way we obtain examples of LDPC codes
with a certain girth. Finally, we extend our constructions to also obtain
irregular LDPC codes.
