TY - GEN
T1 - Linear programming bounds for entanglement-assisted quantum codes
AU - Lai, Ching-Yi
AU - Ashikhmin, Alexei
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/8/9
Y1 - 2017/8/9
N2 - In this paper, we define two split weight enumerators for general quantum codes with entanglement assistance, including nonadditive codes. We show that they obey a MacWilliams identity, which allows us to prove algebraic linear programming bounds, such as the Singleton bound, the Hamming bound, and the first linear programming bound. On the other hand, we derive additional constraints on the size of Pauli subgroups for quantum codes, which helps to improve the linear programming bounds on the minimum distance of quantum codes of small length.
AB - In this paper, we define two split weight enumerators for general quantum codes with entanglement assistance, including nonadditive codes. We show that they obey a MacWilliams identity, which allows us to prove algebraic linear programming bounds, such as the Singleton bound, the Hamming bound, and the first linear programming bound. On the other hand, we derive additional constraints on the size of Pauli subgroups for quantum codes, which helps to improve the linear programming bounds on the minimum distance of quantum codes of small length.
UR - http://www.scopus.com/inward/record.url?scp=85034088305&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2017.8007120
DO - 10.1109/ISIT.2017.8007120
M3 - Conference contribution
AN - SCOPUS:85034088305
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 3200
EP - 3204
BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017
Y2 - 25 June 2017 through 30 June 2017
ER -