The linear time encoding scheme fails to encode

We point out an error in the paper "Linear Time Encoding of LDPC Codes" (by Jin Lu and José M. F. Moura, IEEE Trans). The paper claims to present a linear time encoding algorithm for every LDPC code. We present a family of counterexamples, and point out where the analysis fails. The algorithm in the aforementioned paper fails to encode our counterexample, let alone in linear time.