Subfield subcodes of Reed-Solomon codes and their duals, BCH codes, have been widely used for constructing quantum error-correcting codes with good parameters. In this paper, we study subfield subcodes of projective Reed-Solomon codes and their duals, we provide bases for these codes and estimate their parameters. With this knowledge, we can construct symmetric and asymmetric entanglement-assisted quantum error-correcting codes, which in many cases have new or better parameters than the ones available in the literature.

翻译：Reed-Solomon码及其对偶码BCH码的子域子码已被广泛用于构造具有良好参数的量子纠错码。本文研究射影Reed-Solomon码及其对偶码的子域子码，给出了这些码的基并估计了其参数。基于此知识，我们能够构造出对称与非对称纠缠辅助量子纠错码，这些码在多个情形下具有优于现有文献的新参数或更优参数。