Xing–Ling codes, duals of their subcodes, and good asymmetric quantum codes

• Main Authors: Ezerman, Martianus Frederic, Jitman, Somphong, Solé, Patrick
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2019
• Subjects: Asymmetric Quantum Codes; CSS Codes; DRNTU::Science::Mathematics
• Online Access: https://hdl.handle.net/10356/100747; http://hdl.handle.net/10220/48579
• Institution: Nanyang Technological University

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.