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

We prove that nonbinary quantum stabilizer codes with parameters [[n, k, d]](p) = [[6, 2, 3]](p) and [[7, 3, 3]](p) exist for all odd primes p by using graph machinary, given by Schlingemann and Werner, with a little number theory and combinatorics.