This paper is devoted to studying the symmetric 2-adic complexity of sequences with optimal autocorrelation magnitude and period 8q, where q is a prime satisfying q ≡ 5 (mod 8). These sequences were constructed by interleaving technique from Ding-Helleseth-Martinsen sequences and almost perfect binary sequences. They were presented by Krengel and Ivanov in 2016 and have been proved to have high linear complexity. Our result shows that they also have high symmetric 2-adic complexity.

中文翻译：

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具有最佳自相关幅度和长度 8q 的序列的对称 2-adic 复杂度

本文致力于研究具有最佳自相关幅度和周期为 8 q的序列的对称 2-adic 复杂度，其中q是满足q ≡ 5 (mod 8)的素数。这些序列是由Ding-Helleseth-Martinsen序列和几乎完美的二进制序列通过交织技术构建的。它们由 Krengel 和 Ivanov 在 2016 年提出，并已被证明具有很高的线性复杂度。我们的结果表明它们也具有高对称 2-adic 复杂度。