  The linear complexity is a measure for the unpredictability of a sequence
over a finite field and thus for its suitability in cryptography. In 2012, Diem
introduced a new figure of merit for cryptographic sequences called expansion
complexity. We study the relationship between linear complexity and expansion
complexity. In particular, we show that for purely periodic sequences both
figures of merit provide essentially the same quality test for a sufficiently
long part of the sequence. However, if we study shorter parts of the period or
nonperiodic sequences, then we can show, roughly speaking, that the expansion
complexity provides a stronger test. We demonstrate this by analyzing a
sequence of binomial coefficients modulo $p$. Finally, we establish a
probabilistic result on the behavior of the expansion complexity of random
sequences over a finite field.
