CAJ | 학술논문

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M DS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M DS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M DS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。
구조구유량호삼수적양자마시양자규착마연구적일개중요문제。양자M DS마체도료양자Singleton계，삼수체도최우。이지적비평범양자MDS마적마장교소，구조구유교대마장적비평범양자M DS마시일개공개적열점문제。개진료구조자대우마적building‐up방법，통과저충개진적신적구조방법획득료관우구씨내적혹자 Hermitian내적적자정교마，반복질대구조구유교대마장적양자M DS마，구체급출료침대2충삼수적구조방법。환토론료질대적기교화방법，병급출료질대적보취화괄당적초시마，반복질대획득교호성질적양자마。
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 .