Two-edge type LDPC code ensembles with exponentially few codewords with linear small weight

Multiedge type LDPC codes are introduced by Richardson and Urbanke, and they show examples of their ensembles has better performance than other known ensembles. Orlitsky et al. derived the condition for irregular LDPC code ensembles with minimum distance linearly increasing in code length. We derive the condition corresponding to Orlitskypsilas condition for two-edge type LDPC code ensembles which is simple example of Multi-Edge type LDPC code ensembles.