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

Dazhou Wang and Xiaoping Shi ()
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Dazhou Wang: Department of Mathematics, Gansu Normal University for Nationalities, Hezuo 747000, China
Xiaoping Shi: Department of Mathematics, Gansu Normal University for Nationalities, Hezuo 747000, China

Mathematics, 2025, vol. 13, issue 11, 1-7

Abstract: In this paper, using the interleaving technique, we present a method for constructing M -ary sequences of length 4 N . 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 2 N , 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 2 N where N = 4 f + 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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