由EGRS码构造的量子MDS码

Quantum MDS Codes Constructed by EGRS Codes

摘要: 本文针对量子纠错领域中量子最大距离可分(MDS)码的构造问题展开研究，量子MDS码是一类达到量子Singleton界的最优码，在量子计算与通信中具有重要应用价值。为了突破现有构造方法在码长和参数灵活性上的限制，本文提出了一种创新性的构造：利用两个已知的埃尔米特(Hermitian)自正交扩展广义里德–所罗门(EGRS)码，通过特定的条件组合，来构造一个新的Hermitian自正交EGRS码。利用这一关键结论，我们获得了若干类新的q元量子MDS码。我们构造的量子MDS码的码长与以往的码有很大不同，且参数灵活。本研究不仅为量子MDS码的构造理论提供了新的思路和工具，也为实际量子信息系统中纠错码的设计提供了更多可能性。

Abstract: This article focuses on the construction of quantum Maximum Distance Separable (MDS) codes in the field of quantum error correction. MDS codes are a class of optimal codes that reach the quantum Singleton boundary and have important application value in quantum computing and communication. In order to overcome the limitations of existing construction methods in terms of code length and parameter flexibility, this paper proposes an innovative construction method: using two known Hermitian self-orthogonal Extended Generalized Reed Solomon (EGRS) codes, a new Hermitian self-orthogonal EGRS code is constructed through specific condition combinations. By utilizing this key conclusion, we have obtained several new classes of q-ary quantum MDS codes. The code length of the quantum MDS code we constructed is significantly different from previous codes, and the parameters are flexible. This study not only provides new ideas and tools for the construction theory of quantum MDS codes, but also offers more possibilities for the design of error correction codes in practical quantum information systems.