A construction of quantum LDPC codes from Cayley graphs

The proof of Proposition VI.2 was inaccurate. This issue is addressed in the present version.International audienceWe study a construction of Quantum LDPC codes proposed by MacKay, Mitchison and Shokrollahi in the draft [6]. It is based on the Cayley graph of F_2^n 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(dn^2) 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 [[2^{n-1}, 2^{n/2}, 2^{n/2-1}]]