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August  2017, 11(3): 445-452. doi: 10.3934/amc.2017037

## Integer-valued Alexis sequences with large zero correlation zone

 Department of Electronic Engineering, Southern Taiwan University of Science and Technology, No. 1, Nan-Tai Street, Yungkang Dist., Tainan City 710, Taiwan

Received  January 2015 Revised  February 2016 Published  August 2017

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.

Citation: Wei-Wen Hu. Integer-valued Alexis sequences with large zero correlation zone. Advances in Mathematics of Communications, 2017, 11 (3) : 445-452. doi: 10.3934/amc.2017037
##### References:
 [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. Google Scholar [2] M. Antweiler, Perfect energy efficient sequences, IET Electr. Lett., 27 (2002), 1332-1334. Google Scholar [3] F. Hu, P. Z. Fan, M. Darnell and F. Jin, Binary sequences with good aperiodic autocorrelation functions obtained by neural network search, IET Electr. Lett., 33 (1997), 688-690. Google Scholar [4] J.-W. Jang, Y.-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. Google Scholar [5] H. D. Luke, Binary Alexis sequences with perfect correlation, IEEE Trans. Commu., 49 (2001), 966-968. Google Scholar [6] H. D. Luke, D. 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. Google Scholar [7] Z. Yang and P. H. Ke, Quaternary sequences with odd period and low autocorrelation, Electr. Lett., 46 (2010), 1068-1069. Google Scholar

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##### References:
 [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. Google Scholar [2] M. Antweiler, Perfect energy efficient sequences, IET Electr. Lett., 27 (2002), 1332-1334. Google Scholar [3] F. Hu, P. Z. Fan, M. Darnell and F. Jin, Binary sequences with good aperiodic autocorrelation functions obtained by neural network search, IET Electr. Lett., 33 (1997), 688-690. Google Scholar [4] J.-W. Jang, Y.-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. Google Scholar [5] H. D. Luke, Binary Alexis sequences with perfect correlation, IEEE Trans. Commu., 49 (2001), 966-968. Google Scholar [6] H. D. Luke, D. 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. Google Scholar [7] Z. Yang and P. H. Ke, Quaternary sequences with odd period and low autocorrelation, Electr. Lett., 46 (2010), 1068-1069. Google Scholar
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
 $N_a$ 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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