In this article, new regular incidence structures are presented. They arise
from sets of conics in the affine plane blown-up at its rational points. The
LDPC codes given by these incidence matrices are studied. These sparse
incidence matrices turn out to be redundant, which means that their number of
rows exceeds their rank. Such a feature is absent from random LDPC codes and is
in general interesting for the efficiency of iterative decoding. The
performance of some codes under iterative decoding is tested. Some of them turn
out to perform better than regular Gallager codes having similar rate and row
weight.Comment: 31 pages, 10 figure