Quantum self-dual codes and symmetric matrices

In a recent paper Calderbank, Rains, Shor and Sloane [1] described a method of constructing quantum-error-correcting codes from ordinary binary or quaternary codes that are selforthogonal with respect to a certain inner product. We use this relation to show that a class of binary formally self-dual codes defined by symmetric matrices give rise to quantum codes with error-correcting capacity proportional to the code length.