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 b(dx−1)/2c bit-flip errors and up to b(dz−1)/2c 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.