Small weight codewords in LDPC codes defined by (dual) classical generalized quadrangles
Designs, Codes and Cryptography
ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
On the Minimum Weight of Simple Full-Length Array LDPC Codes
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Reversible low-density parity-check codes
IEEE Transactions on Information Theory
Minimum distance and pseudodistance lower bounds for generalised LDPC codes
International Journal of Information and Coding Theory
Spectral graph analysis of quasi-cyclic codes
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
The minimum distance of graph codes
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
| Hi-index | 754.90 |
The parity-check matrix of a linear code is used to define a bipartite code constraint (Tanner) graph in which bit nodes are connected to parity-check nodes. The connectivity properties of this graph are analyzed using both local connectivity and the eigenvalues of the associated adjacency matrix. A simple lower bound on the minimum distance of the code is expressed in terms of the two largest eigenvalues. For a more powerful bound, local properties of the subgraph corresponding to a minimum-weight word in the code are used to create an optimization problem whose solution is a lower bound on the code's minimum distance. Linear programming gives one bound. The technique is illustrated by applying it to sparse block codes with parameters [7,3,4] and [42,23,6]