基于Hermitian曲线上两点因子的非二元量子码
Nonbinary Quantum Codes from Two-Point Divisors on Hermitian Curves
摘要：
Sarvepalli和Klappenecker展示了如何使用厄米曲线上的经典单点码来构造量子码。Homma和Kim确定了一个更大的代码族的参数，即两点代码。在量子纠错中，在某些量子信道中观察到的不对称性的存在导致了对非对称量子码（AQECC）的研究，其中我们不再假设不同类型的错误是等概率的。本文研究了由两点码构造的量子码。在非对称的情况下，我们严格的改进，在所有可能的有限域的范围内的设计距离。我们从单点编码中产生了大尺寸的纯AQECC和小尺寸的非纯AQECC，它们的参数比AQECC更好。用F16和F64上厄米曲线的数值结果来说明增益。
英文摘要：
Sarvepalli and Klappenecker showed how classical one-point codes on the Hermitian curve can be used to construct quantum codes. Homma and Kim determined the parameters of a larger family of codes, the two-point codes. In quantum error-correction, the observed presence of asymmetry in some quantum channels led to the study of asymmetric quantum codes (AQECCs) where we no longer assume that the different types of errors are equiprobable. This paper considers quantum codes constructed from the two-point codes. In the asymmetric case, we show strict improvements over all possible finite fields for a range of designed distances. We produce large dimension pure AQECC and small dimension impure AQECC that have better parameters than AQECC from one-point codes. Numerical results for the Hermitian curves over F16 and F64 are used to illustrate the gain.
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