发表机构
UAE University（阿联酋大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出单生成元准循环码最小距离的下界，通过穿孔和缩短构造，应用于搜索获得改进的Hermitian LCD码及最大纠缠纠缠辅助量子码。
AI 中文摘要
我们引入了任意指标的单生成元准循环码最小距离的下界，这些下界通过在块级别对码进行穿孔和缩短而获得。对于平衡码，这些界构成一个非递减链，其第一项是Jensen界。我们应用这些界进行计算机搜索，并获得了许多具有良好参数的Hermitian LCD码。其中，有六个长度不超过30的码改进了Araya和Harada的相应下界。这些码进一步给出了最大纠缠的纠缠辅助量子码，我们将这些码与文献中目前记录的参数进行了比较。
英文摘要
We introduce lower bounds on the minimum distance of one-generator quasi-cyclic codes of arbitrary index, obtained by puncturing and shortening the code at the level of its blocks. For balanced codes, these bounds form a nondecreasing chain whose first term is the Jensen bound. We apply these bounds to conduct a computer search and obtain many Hermitian LCD codes with good parameters. Among them there are six codes of length at most 30 which improve the corresponding lower bounds of Araya and Harada. These codes further give maximal-entanglement entanglement-assisted quantum codes, which we compare with the parameters currently recorded in the literature.
