A Note on the Minimum Distance of Quantum LDPC Codes

Abstract

We provide a new lower bound on the minimum distance of a family of quantum LDPC codes based on Cayley graphs proposed by MacKay, Mitchison and Shokrollahi [13]. Our bound is exponential, improving on the quadratic bound of Couvreur, Delfosse and Zémor [3]. This result is obtained by examining a family of subsets of the hypercube which locally satisfy some parity conditions.