The properties of $h$-periodic sequences

The notion of a sequence $h$-periodicity is introduced with a function $h$ mapping the set of words composing the sequence into a set. The properties of $h$-periodic sequences are investigated. In the case of additive $h$ a connection between the period length and the $h$-period length of a sequence is established, and the $h$-period length of linear recurring sequences and of de Bruijn sequences are determined. It is stated that cryptoproperties of some gamma generators depend on $h$-period length of control sequence where $h$ is the function marking the symbols of the sequence.