Correlation measure, linear complexity and maximum order complexity for families of binary sequences.

The correlation measure of order k is an important measure of pseudorandomness for binary sequences. This measure tries to look for dependence between several shifted versions of a sequence. We study the relation between the correlation measure of order k and two other 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. [ABSTRACT FROM AUTHOR]