In the first part of this two-part paper, we construct a family MFD$_2$ of low-correlation quaternary spreading codes having period $2046$. By quaternary, we mean that the spreading code symbols are drawn from $Z_4$ and are designed to be used in conjunction with QPSK modulation. Apart from low auto and crosscorrelation properties, we also require in addition, to our knowledge for the first time, that the spreading code family IZ4$_2$ obtained by taking the union of the component in-phase and quadrature-phase binary spreading codes associated to each quaternary spreading code in MFD$_2$, also have desirable low-correlation properties. We also investigate the balance of the quaternary and binary spreading codes. The second part is motivated by an application to the design of spreading code, (in this application termed as ranging codes), having parameters suitable for use in a lunar PNT system. Two lengths that are of particular current interest for a planned lunar PNT satellite system are $2046$ and $10230$. We study the applicability of a subset IZ4$_{2S}$ of IZ4$_2$ containing balanced binary spreading codes having length $2046$ to such a lunar PNT system. We show that the spreading codes belonging to IZ4$_{2S}$ compare favorably with the spreading codes of length $2046$ appearing in a recent issue of Inside GNSS. We also show that the IZ4$_{10}$ spreading code family in which the spreading codes have length $10230$, compares well in comparison with spreading codes of length $10230$ described in this article. In addition, the IZ4$_{10}$ and IZ4$_2$ spreading codes have been paired so as to be orthogonal at zero shift despite their different lengths and chipping rates.

翻译：在这篇由两部分组成的论文的第一部分中，我们构建了一个具有低相关性的四进制扩频码族MFD$_2$，其周期为$2046$。所谓四进制，是指扩频码符号取自$Z_4$，并设计用于与QPSK调制结合使用。除了低自相关和低互相关特性外，据我们所知，我们首次额外提出了一个要求：通过取MFD$_2$中每个四进制扩频码相关联的同相和正交相位分量二进制扩频码的并集，所获得的扩频码族IZ4$_2$也应具有理想的低相关性特性。我们还研究了这些四进制和二进制扩频码的平衡性。论文的第二部分受到一项具体应用的启发，该应用旨在设计参数适用于月球PNT（定位、导航与授时）系统的扩频码（在此应用中称为测距码）。对于一个计划中的月球PNT卫星系统，目前特别关注的两个码长为$2046$和$10230$。我们研究了IZ4$_2$的一个子集IZ4$_{2S}$（包含长度为$2046$的平衡二进制扩频码）在此类月球PNT系统中的适用性。我们证明，属于IZ4$_{2S}$的扩频码与近期一期《Inside GNSS》中出现的长度为$2046$的扩频码相比具有优势。我们还证明，扩频码长度为$10230$的IZ4$_{10}$扩频码族，与本文描述的其它长度为$10230$的扩频码相比表现良好。此外，尽管IZ4$_{10}$和IZ4$_2$扩频码具有不同的长度和码片速率，但它们已被配对，从而在零偏移时实现正交。