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

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1 Author(s)
Keqin Feng ; Dept. of Math. Sci., Tsinghua Univ., Beijing, China

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 machinery, given by Schlingemann and Werner(see Phys. Rev. A, vol.65, no.012308, 2001), with a little number theory and combinatorics.

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Information Theory, IEEE Transactions on  (Volume:48 ,  Issue: 8 )