The 4-Adic Complexity of A Class of Quaternary Cyclotomic Sequences with Period 2p

2020/11/24 by Shiyuan Qiang, Yan Li, Qiang, Shiyuan +5 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.2011.11875

openalex publication_date 2020/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In cryptography, we hope a sequence over ℤ_m with period N having larger m-adic complexity. Compared with the binary case, the computation of 4-adic complexity of knowing quaternary sequences has not been well developed. In this paper, we determine the 4-adic complexity of the quaternary cyclotomic sequences with period 2p defined in [6]. The main method we utilized is a quadratic Gauss sum G_p valued in ℤ_4^N-1 which can be seen as a version of classical quadratic Gauss sum. Our results show that the 4-adic complexity of this class of quaternary cyclotomic sequences reaches the maximum if 5\nmid p-2 and close to the maximum otherwise.

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