广义Roth-Lempel码的Galois壳及其在EAQECCs中的应用
Galois Hulls of Generalized Roth-Lempel Codes and Their Applications to EAQECCs
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中文总结 AI 辅助
本文提出基于归一化拉格朗日系数的通用方法，构造具有指定Galois壳维数的广义Roth-Lempel码，并应用于纠缠辅助量子纠错码，获得MDS/AMDS码及最大纠缠EAQECCs。
中文摘要 AI 辅助
Galois壳的维数是构造纠缠辅助量子纠错码中的一个重要参数。本文研究了在任意特征有限域上具有指定Galois壳维数的广义Roth-Lempel（GRL）码。我们基于归一化拉格朗日系数和适当的列乘子选择，开发了一种通用的构造方法，并从乘法陪集、迹纤维、加法子空间陪集以及混合加法-乘法纤维中获得了六种显式构造。对于扩展规模$s=2$和$s=3$，我们构造了具有特定维数Galois壳的MDS和AMDS GRL码。所得码提供了具有显式维数、纠缠消耗和相对较大最小距离的EAQECCs。取零维壳还可得到Hermitian LCD GRL码及相应的最大纠缠EAQECCs。
英文摘要
The dimension of a Galois hull is an important parameter in the construction of entanglement-assisted quantum error-correcting codes. In this paper, we study generalized Roth-Lempel (GRL) codes with prescribed Galois hull dimensions over finite fields of arbitrary characteristic. We develop a common construction method based on normalized Lagrange coefficients and suitable choices of column multipliers, and obtain six explicit constructions from multiplicative cosets, trace fibers, additive-subspace cosets, and mixed additive--multiplicative fibers. For extension sizes $s=2$ and $s=3$, we construct MDS and AMDS GRL codes with Galois hulls of specific dimensions. The resulting codes provide EAQECCs with explicit dimension, entanglement consumption, and relatively large minimum distance. Taking zero-dimensional hulls also gives Hermitian LCD GRL codes and the corresponding maximally entangled EAQECCs.
发表机构
- School of Mathematics, Nanjing Normal University（南京师范大学数学学院）
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