A New Method to Compute the 2-Adic Complexity of Binary Sequences
A New Method to Compute the 2-Adic Complexity of Binary Sequences
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DOI：
10.1109/tit.2014.2304451
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发表时间：
2013-09
影响因子：
2.5
通讯作者：
Hai Xiong;Longjiang Qu;C. Li
中科院分区：
文献类型：
--
作者：
Hai Xiong;Longjiang Qu;C. Li
本文提出了一种计算伪随机序列2-adic复杂度的新方法。利用该方法，可以统一地确定所有已知的具有理想二阶自相关的序列的2-adic复杂度。结果表明，它们的2-adic复杂度等于它们的周期。换句话说，它们的2-adic复杂度达到最大。此外，还研究了两类周期为N <$1mod4的最优自相关序列，即Legendre序列和Ding-Helleseth-Lam序列的2-adic复杂度.该方法也可用于计算二元序列作为其他有限域上序列的线性复杂度。
In this paper, a new method is presented to compute the 2-adic complexity of pseudo-random sequences. With this method, the 2-adic complexities of all the known sequences with ideal 2-level autocorrelation are determined in a unified way. Results show that their 2-adic complexities equal their periods. In other words, their 2-adic complexities attain the maximum. In addition, 2-adic complexities of two classes of optimal autocorrelation sequences with period N ≡ 1mod4, namely Legendre sequences and Ding-Helleseth-Lam sequences, are investigated. This method also can be used to compute the linear complexity of binary sequences regarded as sequences over other finite fields.