Correlation measure of order $k$ is an important measure of randomness in binary sequences. This measure tries to look for dependence between several shifted version of a sequence. We study the relation between the correlation measure of order $k$ and another two pseudorandom measures: the $N$th linear complexity and the $N$th maximum order complexity. We simplify and improve several state-of-the-art lower bounds for these two measures using the Hamming bound as well as weaker bounds derived from it.

翻译：排序的关联度量 $k$是衡量二进制序列随机性的重要尺度。 此度量试图寻找一个序列的若干变换版本之间的依赖性。 我们研究了顺序的相对度量 $k$与另外两种假随机度度的关联度之间的关系: 美元线性复杂度和美元最高顺序复杂度。 我们利用哈明约束以及从中得出的较弱界限,简化和改进了这两种测量的几种最先进的下限。