  We show that local correlators in a wide class of kicked chains can be
calculated exactly at light cone edges. Extending previous works on
dual-unitary systems, the correlators between local operators are expressed
through the expectation values of transfer matrices $T$ with small dimensions.
Contrary to the previous studies, our results are not restricted to
dual-unitary systems with spatial-temporal symmetry of the dynamics. They hold
for a generic case without fine tuning of model parameters. The results are
exemplified on the kicked Ising spin chain model, where we provide an explicit
formula for two-point correlators near light cone edges beyond the dual-unitary
regime.
