论文标题
来自矩阵 - 产品代码与准正交和准空间矩阵有关的量子误差校正代码
Quantum error-correcting codes from matrix-product codes related to quasi-orthogonal and quasi-unitary matrices
论文作者
论文摘要
有限字段上的矩阵 - 产品代码是一类重要的长线性代码类，通过将几个相称的较短线性代码与有限字段上的定义矩阵相结合。在有限场上具有某些自我执行性的矩阵产品代码的构建是获得较大长度的良好$ q $ - 量子代码的有效方法。本文有两个目的：第一个是总结本文作者及其合作者在[10-12]中获得的一些结果；第二个是在准正交矩阵（分别为Quasi-Nitary矩阵），欧几里得双含双含量（分别含Hermitian双重含量）矩阵 - 产物代码和$ q $ Q $ - 元素量子代码中添加一些新结果。
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain self-orthogonality over finite fields is an effective way to obtain good $q$-ary quantum codes of large length. This article has two purposes: the first is to summarize some results of this topic obtained by the author of this article and his cooperators in [10-12]; the second is to add some new results on quasi-orthogonal matrices (resp. quasi-unitary matrices), Euclidean dual-containing (resp. Hermitian dual-containing) matrix-product codes and $q$-ary quantum codes derived from these matrix-product codes.
