A quaternary sequence is said to be optimal if its odd-periodic autocorrelation magnitude equal to 2 for even length, and 1 for odd length. In this paper, we propose three constructions of optimal quaternary sequences: the first construction applies the inverse Gray mapping to four component binary sequences, which could be chosen from GMW sequence pair, twin-prime sequence pair, Legendre sequence pair, and ideal sequences; the second one generates optimal sequences from quaternary sequences with optimal even-periodic autocorrelation magnitude; the third one gives new optimal quaternary sequences by applying the sign alternation transform and Gray mapping to GMW sequence pair and twin-prime sequence pair. In particular, some proposed sequences have new parameters.
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The work of Y. Yang was supported by the National Science Foundation of China under grants 61771016 and 61661146003, and the Sichuan Science and Technology Program under Grant 2018JY0046. The work of C. Li was supported by the research project (No. 720025) from UH-nett Vest in Norway, the Research Council of Norway (No. 2477421O70) and the National Natural Science Foundation of China under Grant (No. 61771021).
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This article is part of the Topical Collection on Special Issue on Sequences and Their Applications
Guest Editors: Tor Helleseth, Wai Ho Mow and Zhengchun Zhou
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Yang, Y., Li, C. New quaternary sequences with optimal odd-periodic autocorrelation magnitude. Cryptogr. Commun. 12, 363–374 (2020). https://doi.org/10.1007/s12095-019-00407-0
- Odd-periodic autocorrelation
- Sign alternation transformation
- Quaternary sequences
- Ideal sequence
- Gray mapping
Mathematics Subject Classification (2010)