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Integer-valued Alexis sequences with large zero correlation zone

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  • In this paper, a new class of integer-valued Alexis sequences with length N = 2 (mod 4) is proposed and constructed by using integer-valued almost-perfect sequences obtained from three integer-valued elementary sequences. Compared with binary Alexis sequences, the proposed integer-valued Alexis sequences have a larger zero correlation zone (ZCZ). In addition, the maximal energy efficiency of the proposed sequences is investigated.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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  • Table 1.  Comparisons of ZCZ between binary and proposed sequences

    $N_a$ binary Alexis sequences [1] integer-valued Alexis sequences
    10 4 5
    14 5 6
    18 7 8
    22 8 10
    26 8 12
    30 unknown 14
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  • [1] R. Alexis, Search for sequences with autocorrelation, Proc. Int. Coll. Coding Theory Appl., 49 (1986), 159-172.  doi: 10.1007/3-540-19368-5_18.
    [2] M. Antweiler, Perfect energy efficient sequences, IET Electr. Lett., 27 (2002), 1332-1334. 
    [3] F. HuP. Z. FanM. Darnell and F. Jin, Binary sequences with good aperiodic autocorrelation functions obtained by neural network search, IET Electr. Lett., 33 (1997), 688-690. 
    [4] J.-W. JangY.-S. Kim and S.-H. Kim, New design of quaternary LCZ and ZCZ sequence set from binary LCZ and ZCZ sequence set, Adv. Math. Commun., 3 (2009), 115-124.  doi: 10.3934/amc.2009.3.115.
    [5] H. D. Luke, Binary Alexis sequences with perfect correlation, IEEE Trans. Commu., 49 (2001), 966-968. 
    [6] H. D. LukeD. Schotten and H. Hadinejad-Mahram, Binary and quadriphase sequences with optimal autocorrelation properties: A survey, IEEE Trans. Inf. Theory, 49 (2003), 3271-3282.  doi: 10.1007/978-1-4612-0873-0.
    [7] Z. Yang and P. H. Ke, Quaternary sequences with odd period and low autocorrelation, Electr. Lett., 46 (2010), 1068-1069. 
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