A 3-phase Golay complementary triad (GCT) is a set of three sequences over the 3-phase alphabet {1, ω, ω²}, where \(\omega =e^{\frac {2\pi \sqrt {-1}}{3}}\) is a 3rd root of unity, whose aperiodic autocorrelations sum up to zero for each out-of-phase non-zero time-shifts. Recent results by Avis and Jedwab proved the non-existence of 3-phase GCTs of length N ≡ 4 (mod 6). In this paper, we introduce 3-phase Z-complementary triads (ZCTs) and almost-complementary triads (ACTs). We present systematic constructions of 3-phase ZCTs for various lengths including the case when N ≡ 4 (mod 6). We also analyse the peak-to-mean envelope power ratio (PMEPR) upper-bounds of the proposed ZCTs and ACTs.

三相 Golay 互补三元组 (GCT) 是三相字母表 {1, ω , ω ² } 上的一组三个序列，其中\(\omega =e^{\frac {2\pi \sqrt {- 1}}{3}}\)是 3 次单位根，对于每个异相非零时移，其非周期性自相关总和为零。Avis 和 Jedwab 的最新结果证明不存在长度为N ≡ 4 (mod 6)的三相 GCT 。在本文中，我们介绍了三相 Z 互补三元组 (ZCT) 和几乎互补的三元组 (ACT)。我们提出了各种长度的三相 ZCT 的系统构造，包括N ≡ 4 (mod 6) 的情况。我们还分析了所提出的 ZCT 和 ACT 的峰均包络功率比 (PMEPR) 上限。