  In this paper we construct low-density parity-check (LDPC) codes from
transversal designs with low error-floors over the additive white Gaussian
noise (AWGN) channel. The constructed codes are based on transversal designs
that arise from sets of mutually orthogonal Latin squares (MOLS) with cyclic
structure. For lowering the error-floors, our approach is twofold: First, we
give an exhaustive classification of so-called absorbing sets that may occur in
the factor graphs of the given codes. These purely combinatorial substructures
are known to be the main cause of decoding errors in the error-floor region
over the AWGN channel by decoding with the standard sum-product algorithm
(SPA). Second, based on this classification, we exploit the specific structure
of the presented codes to eliminate the most harmful absorbing sets and derive
powerful constraints for the proper choice of code parameters in order to
obtain codes with an optimized error-floor performance.
