  We consider the problem of constructing $(3,L)$ quasi-cyclic low-density
parity-check (LDPC) codes from complete protographs. A complete protograph is a
small bipartite graph with two disjoint vertex sets such that every vertex in
the variable-node set is connected to every vertex in the check-node set by a
unique edge. This paper analyzes the required lifting factor for achieving
girths of six or eight in the resulting quasi-cyclic codes with constraints on
lifting. The required lifting factors provide lower bounds on the block-length
of such codes.
