  A new method for the construction of the binary quantum stabilizer codes is
provided, where the construction is based on Abelian and non-Abelian groups
association schemes. The association schemes based on non-Abelian groups are
constructed by bases for the regular representation from U6n, T4n, V8n and
dihedral D2n groups. By using Abelian group association schemes followed by
cyclic groups and non-Abelian group association schemes a list of binary
stabilizer codes up to 40 qubits is given in tables 4, 5, and 10. Moreover,
several binary stabilizer codes of distances 5 and 7 with good quantum
parameters is presented. The preference of this method specially for Abelian
group association schemes is that one can construct any binary quantum
stabilizer code with any distance by using the commutative structure of
association schemes
