Xing–Ling codes, duals of their subcodes, and good asymmetric quantum codes
A class of powerful q-ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are q-ary block codes that encode k qudits of quantum information into n qudits and correct up to (dx − 1...
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/100747 http://hdl.handle.net/10220/48579 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | A class of powerful q-ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are q-ary block codes that encode k qudits of quantum information into n qudits and correct up to (dx − 1)/2 bit-flip errors and up to (dz − 1)/2 phase-flip errors. In many cases where the length (q2 − q)/2 ≤ n ≤ (q2 + q)/2 and the field size q are fixed and for chosen values of dx ∈ {2, 3, 4, 5} and dz ≥ δ, where δ is the designed distance of the Xing–Ling (XL) codes, the derived pure q-ary asymmetric quantum CSS codes possess the best possible size given the current state of the art knowledge on the best classical linear block codes. |
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