Quantum codes [[6, 2, 3]]/sub p/ and [[7, 3, 3]]/sub p/ (p ≥ 3) exist

We prove that nonbinary quantum stabilizer codes with parameters [[n, k, d]]/sub p/ = [[6, 2, 3]]/sub p/ and [[7, 3, 3]]/sub p/ exist for all odd primes p by using graph machinery, given by Schlingemann and Werner(see Phys. Rev. A, vol.65, no.012308, 2001), with a little number theory and combinatorics.