Enumeration results on linear complexity profiles and lattice profiles

We present enumeration results on the linear complexity profile and the related lattice profile, a complexity measure based on Marsaglia's lattice test, of sequences over finite fields. In particular, we calculate the number of sequences with prescribed profiles and analyze the increase frequency, that is the jump complexity analog for the lattice profile. Moreover, we provide some results on sequences with a k-almost perfect linear complexity profile respectively lattice profile. Finally, we present some distribution properties of binary sequences with length N and perfect lattice profile.