High-rate low-density parity check codes based on anti-Pasch affine geometries
Bane V. Vasic · 2003
We introduce a combinatorial construction of regular low-density parity check codes based on balanced incomplete block designs whose bipartite graphs have girth six. Our construction employs a special type of anti-Pasch affine geometry that result in codes having minimum distance of at least six. We are primarily concerned with very high-rate codes and low column weights, but the proposed construction can be used to generate long codes as well as codes of arbitrary column weight.