  The problem of finding code distance has been long studied for the generic
ensembles of linear codes and led to several algorithms that substantially
reduce exponential complexity of this task. However, no asymptotic complexity
bounds are known for distance verification in other ensembles of linear codes.
Our goal is to re-design the existing generic algorithms of distance
verification and derive their complexity for LDPC codes. We obtain new
complexity bounds with provable performance expressed in terms of the
erasure-correcting thresholds of long LDPC codes. These bounds exponentially
reduce complexity estimates known for linear codes.
