  In this paper we analyze the bound on the additive white Gaussian noise
channel (AWGNC) pseudo-weight of a (c,d)-regular linear block code based on the
two largest eigenvalues of H^T H. In particular, we analyze (c,d)-regular
quasi-cyclic (QC) codes of length rL described by J x L block parity-check
matrices with circulant block entries of size r x r. We proceed by showing how
the problem of computing the eigenvalues of the rL x rL matrix H^T H can be
reduced to the problem of computing eigenvalues for r matrices of size L x L.
We also give a necessary condition for the bound to be attained for a circulant
matrix H and show a few classes of cyclic codes satisfying this criterion.
