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Three-phase Z-complementary triads and almost complementary triads

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 611756, China

    Chen Liu, Avik. R. Adhikary & Zhengchun Zhou

  2. Institute of Software Chinese Academy of Sciences, Beijing, China

    Shuaijun Liu

  3. The Key Lab of Information Coding and Transmission, Southwest Jiaotong University, Chengdu, 611756, China

    Xianfu Lei

Authors
  1. Chen Liu
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  2. Shuaijun Liu
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  3. Xianfu Lei
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  4. Avik. R. Adhikary
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  5. Zhengchun Zhou
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Correspondence to Shuaijun Liu.

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Liu, C., Liu, S., Lei, X. et al. Three-phase Z-complementary triads and almost complementary triads. Cryptogr. Commun. 13, 763–773 (2021). https://doi.org/10.1007/s12095-021-00509-8

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  • DOI: https://doi.org/10.1007/s12095-021-00509-8

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