Correlation, Linear Complexity, Maximum order Complexity on Families of binary Sequences

07/25/2021

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by   Zhixiong Chen, et al.

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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 Nth linear complexity and the Nth 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.