标题： 一种使用分量码构造无限自正交准循环码族的方法.pdf 显示英文标题

标题： A Construction of Infinite Families of Self-Orthogonal Quasi-Cyclic Codes Using Constituent Codes.pdf

摘要： 准循环码最近被用于量子纠错码的构造。 在本文中，我们提出了一种无限族准循环码的构造方法，这些码在欧几里得和埃米特内积下是自正交的。 特别是，它们的维数和最小距离的下界是通过定义在域扩张$\mathbb{F}_q$上的构成码来计算的。 我们还证明了最小距离的下界满足类似平方根的下界，并展示了如何从我们的构造中得到自对偶的准循环码。 利用CSS构造，我们证明了具有优良参数的量子纠错码的存在性。 显示英文摘要

摘要： Quasi-cyclic codes have been recently employed in the constructions of quantum error-correcting codes. In this paper, we propose a construction of infinite families of quasi-cyclic codes which are self-orthogonal with respect to the Euclidean and Hermitian inner products. In particular, their dimension and a lower bound for their minimum distance are computed using their constituent codes defined over field extensions of $\mathbb{F}_q$. We also show that the lower bound for the minimum distance satisfies the square-root-like lower bound and also show how self-dual quasi-cyclic codes can arise from our construction. Using the CSS construction, we show the existence of quantum error-correcting codes with good parameters.