Quaternary sequences with high 4-adic complexity have attracted widespread attention in communication and cryptography systems. In this paper, for an odd prime p, several new classes of quaternary sequences with even period 2p are constructed by using the Legendre sequences of period p. And the autocorrelation distribution of the new quaternary sequences is derived. We determine the 4-adic complexity of these new quaternary sequences. The results show that the new quaternary sequences have good autocorrelation properties, and the 4-adic complexity of these new quaternary sequences is large enough to resist the attack of the rational approximation algorithm.

中文翻译：

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具有良好自相关性的新四元序列的4进复杂度

具有高4-adic复杂度的四元序列在通信和密码系统中引起了广泛的关注。本文针对奇素数 p ， 利用周期 p 的勒让德序列构造了几类新的偶数周期为 2 p的四元序列。并推导了新四元序列的自相关分布。我们确定这些新四元序列的 4-adic 复杂度。结果表明，新的四元序列具有良好的自相关特性，并且这些新的四元序列的4进复杂度足够大，足以抵抗有理逼近算法的攻击。