Recently, a class of binary sequences with optimal autocorrelation magnitude has been presented by Su et al. based on Ding-Helleseth-Lam sequences and interleaving technique (Designs, Codes and Cryptography 86, 1329–1338, 2018). The linear complexity of this class of sequences has been proved to be large enough to resist the B-M Algorithm by Fan (Designs, Codes and Cryptography 86, 2441–2450, 2018). 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.

中文翻译：

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具有最佳自相关幅度的二元序列的2-adic复杂度

最近，Su等人提出了一类具有最佳自相关幅度的二进制序列。基于Ding-Helleseth-Lam序列和交织技术（Designs，Codes和Cryptography 86，1329–1338，2018）。Fan证明，此类序列的线性复杂度足以抵御BM算法（Designs，Codes和Cryptography 86，2441-2450，2018）。在本文中，我们研究了周期为4 p的这些序列的2 adic复杂度，并显示它们不小于2 p，即，其2 adic复杂度足以抵御有理逼近算法。