LDPC codes from Singer cycles

The main goal of coding theory is to devise efficient systems to
exploit the full capacity of a communication channel, thus achieving
an arbitrarily small error probability. Low Density Parity Check
(LDPC) codes are a family of block codes---characterised by admitting
a sparse parity check matrix---with good correction capabilities. In
the present paper the orbits of subspaces of a finite projective space
under the action of a Singer cycle are investigated. The incidence matrix associated to each of these structures yields an LDPC code in a natural manner.