四进制码设计的码算术方法及其在（1/64）阶分式中的应用
A code arithmetic approach for quaternary code designs and its application to (1/64)th-fractions
摘要：
在过去的二十年里，对良好的非正则部分析因设计的研究受到了极大的关注。最近的研究表明，从四元码（QC）构造的设计在这方面是非常有前途的。本文旨在探索的基本结构和发展的理论来描述一般$(1/4)^p$ th分数QC设计的字长和别名指数。并将其应用于（1/64）次分式QC设计。给出的例子，表明存在一些QC设计，具有更好的设计性能，从而更具有成本效益，比常规的部分因子设计相同的大小。此外，还给出了关于（1/64）阶QC设计的周期结构与分辨率的关系。
英文摘要：
The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The present paper aims at exploring the fundamental structure and developing a theory to characterize the wordlengths and aliasing indexes for a general $(1/4)^p$th-fraction QC design. Then the theory is applied to (1/64)th-fraction QC designs. Examples are given, indicating that there exist some QC designs that have better design properties, and are thus more cost-efficient, than the regular fractional factorial designs of the same size. In addition, a result about the periodic structure of (1/64)th-fraction QC designs regarding resolution is stated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
