CSS-like constructions of asymmetric quantum codes

• Main Authors: Ezerman, Martianus Frederic, Jitman, Somphong, Ling, San, Pasechnik, Dmitrii V.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2019
• Subjects: DRNTU::Science::Mathematics; Asymmetric Quantum Codes; Best-known Linear Codes
• Online Access: https://hdl.handle.net/10356/100356; http://hdl.handle.net/10220/48582
• Institution: Nanyang Technological University

Asymmetric quantum error-correcting codes (AQCs) may offer some advantage over their symmetric counterparts by providing better error-correction for the more frequent error types. The well-known CSS construction of q-ary AQCs is extended by removing the F q -linearity requirement as well as the limitation on the type of inner product used. The proposed constructions are called CSS-like constructions and utilize pairs of nested subfield linear codes under one of the Euclidean, trace Euclidean, Hermitian, and trace Hermitian inner products. After establishing some theoretical foundations, best-performing CSS-like AQCs are constructed. Combining some constructions of nested pairs of classical codes and linear programming, many optimal and good pure q-ary CSS-like codes for q ∈ {2,3,4,5,7,8,9} up to reasonable lengths are found. In many instances, removing the F q -linearity and using alternative inner products give us pure AQCs with improved parameters than relying solely on the standard CSS construction.