The quad-phase codes of a given length may be organized into equivalence classes relative to a set of operations preserving autocorrelation peak sidelobe level (PSL). Knowledge about these equivalence classes can be exploited for faster searches or for efficient listing of low-$\rm PSL$ codes. This paper is part of an effort to enumerate autocorrelation $\rm PSL$ equivalence classes for quad-phase codes of any length. An earlier paper achieved a formula for the number of $\rm PSL$ equivalence classes for even lengths $N \geq 2$, as well as a simple algorithm for generating equivalence class representatives. This paper completes the enumeration task by extending the same formula to the odd lengths $N \geq 3$. The results make use of work by Yurramendi in enumerating equivalence classes for binary rectangular grids relative to horizontal reflection and vertical reflection. In addition, a method is described for generating a minimal set of $\rm PSL$ equivalence class representatives covering the space of quad-phase codes of any odd length $N > 3$.

中文翻译：

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奇数四相码PSL等价类的枚举和生成

可以将给定长度的四相码组织成相对于一组保持自相关峰值旁瓣电平 (PSL) 的操作的等价类。可以利用有关这些等价类的知识进行更快的搜索或有效地列出低$\rm PSL$代码。这篇论文是枚举自相关的努力的一部分$\rm PSL$任何长度的四相码的等价类。较早的一篇论文实现了一个公式$\rm PSL$ 偶数长度的等价类 $N \geq 2$，以及生成等价类代表的简单算法。本文通过将相同的公式扩展到奇数长度来完成枚举任务$N \geq 3$. 结果利用了 Yurramendi 在枚举二进制矩形网格相对于水平反射和垂直反射的等价类方面的工作。此外，描述了一种用于生成最小集合的方法$\rm PSL$ 覆盖任意奇数长度的四相码空间的等价类代表 $N > 3$.