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The 2-adic complexity of a class of binary sequences with optimal autocorrelation magnitude. (English) Zbl 1453.94053
Summary: Recently, a class of binary sequences with optimal autocorrelation magnitude has been presented by W. Su et al. [Des. Codes Cryptography 86, No. 6, 1329–1338 (2018; Zbl 1387.94060)], based on Ding-Helleseth-Lam sequences and interleaving technique. The linear complexity of this class of sequences has been proved to be large enough to resist the B-M Algorithm by C. Fan [Des. Codes Cryptography 86, No. 10, 2441–2450 (2018; Zbl 1408.94923)]. In this paper, we study the 2-adic complexities of these sequences with period \(4p\) and show they are no less than \(2p\), i.e., its 2-adic complexity is large enough to resist the Rational Approximation Algorithm.

MSC:
94A55 Shift register sequences and sequences over finite alphabets in information and communication theory
11B50 Sequences (mod \(m\))
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
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