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The 4-adic complexity of quaternary sequences with optimal odd-periodic autocorrelation magnitude

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Abstract

Based on the inverse Gray mapping and sign alternation transform, a new family of quaternary sequences with optimal odd-periodic autocorrelation magnitude has been constructed by using the Legendre sequence pair, twin-prime sequence pair and GMW sequence pair. In this paper, we use the correlation properties of the Legendre sequence pair, twin-prime sequence pair and GMW sequence pair to determine the lower bound of 4-adic complexity of these quaternary sequences, as well as show that these quaternary sequences have large 4-adic complexity.

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Authors and Affiliations

  1. Research Center for Number Theory and Its Applications, Northwest University, Xi’an, 710127, China

    Xiaoyan Jing & Zhefeng Xu

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  1. Xiaoyan Jing
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  2. Zhefeng Xu
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Correspondence to Zhefeng Xu.

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This work is supported by the N.S.F.(11971381, 12371007) of P. R. China and Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No. 22JSY007).

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Jing, X., Xu, Z. The 4-adic complexity of quaternary sequences with optimal odd-periodic autocorrelation magnitude. AAECC (2024). https://doi.org/10.1007/s00200-024-00647-5

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  • DOI: https://doi.org/10.1007/s00200-024-00647-5

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