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

Authors:
Keqin Feng
Affiliations:
Dept. of Math. Sci., Tsinghua Univ., Beijing
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

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.