Designs and their codes
Theory of Information and Coding
Theory of Information and Coding
A comparison of known codes, random codes, and the best codes
IEEE Transactions on Information Theory
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
On the complexity of minimum distance decoding of long linear codes
IEEE Transactions on Information Theory
Efficient encoding of low-density parity-check codes
IEEE Transactions on Information Theory
Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
On algebraic construction of Gallager and circulant low-density parity-check codes
IEEE Transactions on Information Theory
Endcoding complexity versus minimum distance
IEEE Transactions on Information Theory
Families of twisted tensor product codes
Designs, Codes and Cryptography
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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.