利用经典码构造大码长量子MDS码

On the construction of quantum MDS codes with large length from classical codes

构造具有良好参数的量子码是量子纠错码研究的一个重要问题.量子MDS码达到了量子Singleton界,参数达到最优.已知的非平凡量子MDS码的码长较小,构造具有较大码长的非平凡量子MDS码是一个公开的热点问题.改进了构造自对偶码的building-up方法,通过这种改进的新的构造方法获得了关于欧氏内积或者Hermitian内积的自正交码,反复迭代构造具有较大码长的量子MDS码,具体给出了针对2种参数的构造方法.还讨论了迭代的技巧和方法,并给出了迭代的步骤和适当的初始码,反复迭代获得较好性质的量子码.

Constructing quantum codes with good parameters is of great importance .Quantum MDS codes meet the Singleton bound ,whose parameters are optimal .However ,the known non‐trifle quantum MDS codes have small length .It is an open question attracting much attention to construct quantum MDS codes with lager length .In this paper ,we improve the building‐up methods for self‐dual codes .With the new methods for two kinds of parameters ,we get the self orthogonal codes with Euclidean or hermitian inner product ,and the quantum MDS codes with lager length are gained by iteration .We also discuss the iteration technique ,and gain the iteration steps and proper initial co des .