论文标题
MDS代码的Galois船体及其量子误差校正
Galois hulls of MDS codes and their quantum error correction
论文作者
论文摘要
线性代码的船体在量子信息和编码理论中起着重要作用。在本文中，通过研究有限场FQ上广义的Reed-Solomon（GRS）代码和扩展的GRS代码的Galois船体，我们提供了几个新的MDS代码家族，其中包括以前未获得的任意维度的Galois船体。其中一些概括了文献中的[13]。结果，使用这些MDS代码与任意维度的Galois船体一起，我们构建了MDS纠缠辅助误差校正校正代码（EAQECC）的九个新家族，具有灵活的参数。
The hull of linear codes plays an important role in quantum information and coding theory. In the present paper, by investigating the Galois hulls of generalized Reed-Solomon (GRS) codes and extended GRS codes over the finite field Fq, we give several new families of MDS codes with Galois hulls of arbitrary dimensions that are not obtained before. Some of them generalize the ones in the literature [13]. As a consequence, using these MDS codes with Galois hulls of arbitrary dimensions, we construct nine new families of MDS entanglement-assisted quantum error-correcting codes (EAQECCs) with flexible parameters.
