lower bound: | 3 |
upper bound: | 3 |
Construction of a [[13,5,3]] quantum code: [1]: [[11, 5, 3]] quantum code over GF(2^2) Construction from a stored generator matrix [2]: [[13, 5, 3]] quantum code over GF(2^2) ExtendCode [1] by 2 stabilizer matrix: [1 0 1 0 1 1 1 1 1 0 0 0 0|0 0 1 0 0 1 0 0 1 1 0 0 0] [0 0 1 0 0 1 0 0 1 1 0 0 0|1 0 0 0 1 0 1 1 0 1 0 0 0] [0 1 1 0 0 1 1 0 0 0 0 0 0|0 0 0 0 0 1 1 1 1 1 1 0 0] [0 0 0 0 0 1 1 1 1 1 1 0 0|0 1 1 0 0 0 0 1 1 1 1 0 0] [0 0 0 1 1 0 0 1 1 1 1 0 0|0 0 0 0 0 1 1 1 1 1 1 0 0] [0 0 0 0 0 1 1 1 1 1 1 0 0|0 0 0 1 1 1 1 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0] last modified: 2011-06-23
The upper bound was shown in
Jürgen Bierbrauer, Richard Fears, Stefano Marcugini, and Fernanda Pambianco,
"The Nonexistence of a [[13,5,4]]-Quantum Stabilizer Code,"
IEEE Transactions on Information Theory, 57(7):4788-4793 (2011).
DOI: 10.1109/TIT.2011.2146430