lower bound: | 4 |
upper bound: | 4 |
Construction of a [[27,15,4]] quantum code: [1]: [[40, 30, 4]] quantum code over GF(2^2) quasicyclic code of length 40 stacked to height 2 with 16 generating polynomials [2]: [[24, 14, 4]] quantum code over GF(2^2) Shortening of [1] at { 3, 5, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 28, 30, 31, 34 } [3]: [[25, 14, 4]] quantum code over GF(2^2) ExtendCode [2] by 1 [4]: [[27, 14, 4]] quantum code over GF(2^2) ExtendCode [3] by 2 stabilizer matrix: [1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0|0 1 0 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0|1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0|1 1 0 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0|0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0|0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0] [0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0|1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0|1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 1 0 0 0] [0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0|1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0|1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0|0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 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 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 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 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 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 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 0] last modified: 2005-06-24
The upper bound was shown in
Ching-Yi Lai and Alexei Ashikhmin,
"Linear Programming Bounds for Entanglement-Assisted Quantum Error-Correcting Codes by Split Weight Enmerators,"
IEEE Transactions on Information Theory, 64(1):622-639 (2018).
DOI: 10.1109/TIT.2017.2711601