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Volume 13
Issue 11
10.3390/math13111808
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Article

New Optimal Quaternary Sequences with Period 2N from Interleaving Tang–Lindner Sequences

by
Dazhou Wang
1 and
Xiaoping Shi
1,2,*
1
Department of Mathematics, Gansu Normal University for Nationalities, Hezuo 747000, China
2
Department of Mathematics, Nanjing Forestry University, Nanjing 210037, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(11), 1808; https://doi.org/10.3390/math13111808
Submission received: 2 April 2025 / Revised: 18 May 2025 / Accepted: 23 May 2025 / Published: 28 May 2025
Versions Notes

Abstract

In this paper, using the interleaving technique, we present a method for constructing M-ary sequences of length 4N. We propose a new concept, referred to as the semi-interleaved sequence, based on some of the special cases of our construction. The period of these semi-interleaved sequences is 2N, and their autocorrelations can be obtained in the same way as those of interleaved sequences. Applying the construction to certain known sequences, we obtain new quaternary sequences having period 2N where N=4f+1 is prime and f is an odd integer. The nontrivial autocorrelations of the new sequences are 2 and −2. From the autocorrelation distributions, we know that the new sequences cannot be obtained by previously known methods.
Keywords: M-ary sequences; autocorrelation; interleaved technique; semi-interleaved sequences; Tang–Lindner sequences M-ary sequences; autocorrelation; interleaved technique; semi-interleaved sequences; Tang–Lindner sequences

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MDPI and ACS Style

Wang, D.; Shi, X. New Optimal Quaternary Sequences with Period 2N from Interleaving Tang–Lindner Sequences. Mathematics 2025, 13, 1808. https://doi.org/10.3390/math13111808

AMA Style

Wang D, Shi X. New Optimal Quaternary Sequences with Period 2N from Interleaving Tang–Lindner Sequences. Mathematics. 2025; 13(11):1808. https://doi.org/10.3390/math13111808

Chicago/Turabian Style

Wang, Dazhou, and Xiaoping Shi. 2025. "New Optimal Quaternary Sequences with Period 2N from Interleaving Tang–Lindner Sequences" Mathematics 13, no. 11: 1808. https://doi.org/10.3390/math13111808

APA Style

Wang, D., & Shi, X. (2025). New Optimal Quaternary Sequences with Period 2N from Interleaving Tang–Lindner Sequences. Mathematics, 13(11), 1808. https://doi.org/10.3390/math13111808

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