Explicit construction of graphs with an arbitrary large girth and of large size
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
IEEE Transactions on Information Theory - Part 1
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Minimum-distance bounds by graph analysis
IEEE Transactions on Information Theory
Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
Quasicyclic low-density parity-check codes from circulant permutation matrices
IEEE Transactions on Information Theory
Explicit construction of families of LDPC codes with no 4-cycles
IEEE Transactions on Information Theory
LDPC block and convolutional codes based on circulant matrices
IEEE Transactions on Information Theory
LDPC codes from generalized polygons
IEEE Transactions on Information Theory
On the Dimensions of Certain LDPC Codes Based on -Regular Bipartite Graphs
IEEE Transactions on Information Theory
Some low-density parity-check codes derived from finite geometries
Designs, Codes and Cryptography
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We find lower bounds on the minimum distance and characterize codewords of small weight in low-density parity check (LDPC) codes defined by (dual) classical generalized quadrangles. We analyze the geometry of the non-singular parabolic quadric in PG(4,q) to find information about the LDPC codes defined by Q (4,q), $${\mathcal{W}(q)}$$ and $${\mathcal{H}(3,q^{2})}$$ . For $${\mathcal{W}(q)}$$ , and $${\mathcal{H}(3,q^{2})}$$ , we are able to describe small weight codewords geometrically. For $${\mathcal{Q}(4,q)}$$ , q odd, and for $${\mathcal{H}(4,q^{2})^{D}}$$ , we improve the best known lower bounds on the minimum distance, again only using geometric arguments. Similar results are also presented for the LDPC codes LU(3,q) given in [Kim, (2004) IEEE Trans. Inform. Theory, Vol. 50: 2378---2388]