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Sarvepalli and Klappenecker showed how classical one-point codes on theHermitian curve can be used to construct quantum codes. Homma and Kimdetermined the parameters of a larger family of codes, the two-point codes. Inquantum error-correction, the observed presence of asymmetry in some quantumchannels led to the study of asymmetric quantum codes (AQECCs) where we nolonger assume that the different types of errors are equiprobable. This paperconsiders quantum codes constructed from the two-point codes. In the asymmetriccase, we show strict improvements over all possible finite fields for a rangeof designed distances. We produce large dimension pure AQECC and smalldimension impure AQECC that have better parameters than AQECC from one-pointcodes. Numerical results for the Hermitian curves over F16 and F64 are used toillustrate the gain.

Nonbinary Quantum Codes from Two-Point Divisors on Hermitian Curves