  Using the Weyl commutation relations over a finite field we introduce a
family of error-correcting quantum stabilizer codes based on a class of
symmetric matrices over the finite field satisfying certain natural conditions.
When the field is GF(2) the existence of a rich class of such symmetric
matrices is demonstrated by a simple probabilistic argument depending on the
Chernoff bound for i.i.d symmetric Bernoulli trials. If, in addition, these
symmetric matrices are assumed to be circulant it is possible to obtain
concrete examples by a computer program. The quantum codes thus obtained admit
elegant encoding circuits.
