A quaternary sequence is said to be optimal if its odd-periodic autocorrelation magnitude equal to 2 for even length, and 1 for odd length. In this paper, we propose three constructions of optimal quaternary sequences: the first construction applies the inverse Gray mapping to four component binary sequences, which could be chosen from GMW sequence pair, twin-prime sequence pair, Legendre sequence pair, and ideal sequences; the second one generates optimal sequences from quaternary sequences with optimal even-periodic autocorrelation magnitude; the third one gives new optimal quaternary sequences by applying the sign alternation transform and Gray mapping to GMW sequence pair and twin-prime sequence pair. In particular, some proposed sequences have new parameters.

中文翻译：

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具有最佳奇周期自相关幅度的新四元序列

如果四进制序列的奇周期自相关幅度对于偶数长度等于2，对于奇数长度等于1，则称其为最佳。在本文中，我们提出了三种最佳四元序列的结构：第一种结构将逆格雷映射应用于四个分量二元序列，可以从GMW序列对，双素数序列对，Legendre序列对和理想序列中进行选择；第二个从具有最佳偶周期自相关幅度的四元序列生成最优序列；第三类通过将符号交替变换和格雷映射应用于GMW序列对和双素数序列对，给出了新的最佳四元序列。特别地，一些提出的序列具有新的参数。