B's goal is to convert the vector to the vector of all zeros. A's goal is to prevent this from ever happening. There is a series of rounds for t=0, 1, ... In the tth round:
If at the beginning of round t, Vt is zero, then B has won. Otherwise the game continues.
B picks an n-bit pattern P.
A circularly shifts P by any amount she wants, then xors the result with the current vector Vt producing Vt+1.