Matrix analysis
Combinatorica
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Semi-Direct Product in Groups and Zig-Zag Product in Graphs: Connections and Applications
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Expander-Based Constructions of Efficiently Decodable Codes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Good expander graphs and expander codes: parameters and decoding
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
On generalized hamming weights and the covering radius of linear codes
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
IEEE Transactions on Information Theory - Part 1
Linear-time encodable and decodable error-correcting codes
IEEE Transactions on Information Theory - Part 1
Introduction to the special issue on codes on graphs and iterative algorithms
IEEE Transactions on Information Theory
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory
Minimum-distance bounds by graph analysis
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
Error exponents of expander codes
IEEE Transactions on Information Theory
Improved Nearly-MDS Expander Codes
IEEE Transactions on Information Theory
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We characterize optimal bipartite expander graphs and give necessary and sufficient conditions for optimality. We determine the expansion parameters of the BIBD graphs and show that they yield optimal expander graphs that are also bipartite Ramanujan graphs. In particular, we show that the bipartite graphs derived from finite projective and affine geometries yield optimal Ramanujan graphs. This in turn leads to a theoretical explanation of the good performance of a class of LDPC codes.