We study a construction of Quantum LDPC codes proposed by MacKay, Mitchison
and Shokrollahi. It is based on the Cayley graph of Fn together with a set of
generators regarded as the columns of the parity-check matrix of a classical
code. We give a general lower bound on the minimum distance of the Quantum code
in O(dn2) where d is the minimum distance of the classical code.
When the classical code is the [n,1,n] repetition code, we are able to
compute the exact parameters of the associated Quantum code which are [[2n,22n+1,22n−1]].Comment: The material in this paper was presented in part at ISIT 2011. This
article is published in IEEE Transactions on Information Theory. We point out
that the second step of the proof of Proposition VI.2 in the published
version (Proposition 25 in the present version and Proposition 18 in the ISIT
extended abstract) is not strictly correct. This issue is addressed in the
present versio