Correlation properties of interleaved Legendre sequences and Ding-Helleseth-Lam sequences

Yixin Ren; Chenyu Hou; Huaning Liu; Yixin Ren; Chenyu Hou; Huaning Liu

doi:10.3934/era.2023232

Electronic Research Archive

2023, Volume 31, Issue 8: 4549-4556. doi: 10.3934/era.2023232

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Research article Special Issues

Correlation properties of interleaved Legendre sequences and Ding-Helleseth-Lam sequences

Research Center for Number Theory and Its Applications, School of Mathematics, Northwest University, Xi'an 710127, China

Received: 03 April 2023 Revised: 24 May 2023 Accepted: 30 May 2023 Published: 19 June 2023

Sequences with optimal autocorrelation properties play an important role in wireless communication, radar and cryptography. Interleaving is a very important method in constructing the optimal autocorrelation sequence. Tang and Gong gave three different constructions of interleaved sequences (generalized GMW sequences, twin prime sequences and Legendre sequences). Su et al. constructed a series of sequences with optimal autocorrelation magnitude via interleaving Ding-Helleseth-Lam sequences. In this paper we further study the correlation properties of interleaved Legendre sequences and Ding-Helleseth-Lam sequences.
- fourth-order,
- correlation,
- interleaving,
- Legendre sequence,
- Ding-Helleseth-Lam sequence
Citation: Yixin Ren, Chenyu Hou, Huaning Liu. Correlation properties of interleaved Legendre sequences and Ding-Helleseth-Lam sequences[J]. Electronic Research Archive, 2023, 31(8): 4549-4556. doi: 10.3934/era.2023232

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Abstract

Sequences with optimal autocorrelation properties play an important role in wireless communication, radar and cryptography. Interleaving is a very important method in constructing the optimal autocorrelation sequence. Tang and Gong gave three different constructions of interleaved sequences (generalized GMW sequences, twin prime sequences and Legendre sequences). Su et al. constructed a series of sequences with optimal autocorrelation magnitude via interleaving Ding-Helleseth-Lam sequences. In this paper we further study the correlation properties of interleaved Legendre sequences and Ding-Helleseth-Lam sequences.

References

[1]	S. W. Golomb, G. Gong, Signal Design for Good Correlation-for Wireless Communication, Cryptography and Radar, Cambridge University Press, Cambridge, 2005. https://doi.org/10.1017/CBO9780511546907
[2]	K. T. Arasu, C. Ding, T. Helleseth, P. V. Kumar, H. Martinsen, Almost difference sets and their sequences with optimal autocorrelation, IEEE Trans. Inf. Theory, 47 (2001), 2934–2943. https://doi.org/10.1109/18.959271 doi: 10.1109/18.959271
[3]	Y. Cai, C. Ding, Binary sequences with optimal autocorrelation, Theor. Comput. Sci., 410 (2009), 2316–2322. https://doi.org/10.1016/j.tcs.2009.02.021 doi: 10.1016/j.tcs.2009.02.021
[4]	D. Jungnickel, Finite Fields: Structure and Arithmetics, BI-Wissenschaftsverlag, Mannheim, 1993.
[5]	A. Lempel, M. Cohn, W. L. Eastman, A class of balanced binary sequences with optimal autocorrelation properties, IEEE Trans. Inf. Theory, 23 (1977), 38–42. https://doi.org/10.1109/TIT.1977.1055672 doi: 10.1109/TIT.1977.1055672
[6]	N. Li, X. Tang, On the linear complexity of binary sequences of period $4N$ with optimal autocorrelation value/magnitude, IEEE Trans. Inf. Theory, 57 (2011), 7597–7604. https://doi.org/10.1109/TIT.2011.2159575 doi: 10.1109/TIT.2011.2159575
[7]	V. M. Sidel'nikov, Some $k$-valued pseudo-random sequences and nearly equidistant codes, Probl. Peredachi Inf., 5 (1969), 12–16.
[8]	W. Su, Y. Yang, C. Fan, New optimal binary sequences with period $4p$ via interleaving Ding-Helleseth-Lam sequences, Des. Codes Cryptogr., 86 (2018), 1329–1338. https://doi.org/10.1007/s10623-017-0398-5 doi: 10.1007/s10623-017-0398-5
[9]	W. Su, Y. Yang, Z. Zhou, X. Tang, New quaternary sequences of even length with optimal auto-correlation, Sci. China Inf. Sci., 61 (2018). https://doi.org/10.1007/s11432-016-9087-2 doi: 10.1007/s11432-016-9087-2
[10]	X. Tang, G. Gong, New constructions of binary sequences with optimal autocorrelation value/magnitude, IEEE Trans. Inf. Theory, 56 (2010), 1278–1286. https://doi.org/10.1109/TIT.2009.2039159 doi: 10.1109/TIT.2009.2039159
[11]	N. Yu, G. Gong, New binary sequences with optimal autocorrelation magnitude, IEEE Trans. Inf. Theory, 54 (2008), 4771–4779. https://doi.org/10.1109/TIT.2008.928999 doi: 10.1109/TIT.2008.928999
[12]	G. gong, Theory and applications of $q$-ary interleaved sequences, IEEE Trans. Inf. Theory, 41 (1995), 400–411. https://doi.org/10.1109/18.370141 doi: 10.1109/18.370141
[13]	C. Ding, T. Helleseth, K. Y. Lam, Several classes of binary sequences with three-level autocorrelation, IEEE Trans. Inf. Theory, 45 (1999), 2606–2612. https://doi.org/10.1109/18.796414 doi: 10.1109/18.796414
[14]	C. Fan, The linear complexity of a class of binary sequences with optimal autocorrelation, Des. Codes Cryptogr., 86 (2018), 2441–2450. https://doi.org/10.1007/s10623-018-0456-7 doi: 10.1007/s10623-018-0456-7
[15]	Y. Sun, T. Yan, Z. Chen, L. Wang, The $2$-adic complexity of a class of binary sequences with optimal autocorrelation magnitude, Cryptogr. Commun., 12 (2020), 675–683. https://doi.org/10.1007/s12095-019-00411-4 doi: 10.1007/s12095-019-00411-4

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