Memory-two zero-determinant strategies in repeated games

Repeated games have provided an explanation how mutual cooperation can be achieved even if defection is more favorable in a one-shot game in prisoner's dilemma situation.
Recently found zero-determinant strategies have substantially been investigated in evolutionary game theory.
The original memory-one zero-determinant strategies unilaterally enforce linear relations between average payoffs of players.
Here, we extend the concept of zero-determinant strategies to memory-two strategies in repeated games.
Memory-two zero-determinant strategies unilaterally enforce linear relations between correlation functions of payoffs and payoffs at the previous round.
Examples of memory-two zero-determinant strategy in the repeated prisoner's dilemma game are provided, some of which generalize the Tit-for-Tat strategy to memory-two case.
Extension of zero-determinant strategies to memory-$n$ case with $n\geq 2$ is also straightforward.