Remote control for actuating garage doors and other barriers, and method and system of using same. A base unit includes: a wireless receiver, to wirelessly receive from an electronic device an incoming wireless signal indicating a command to actuate a garage door; a wireless signal constructor, to dynamically construct an outgoing wireless signal which comprises a rolling code; a wireless transmitter, to transmit the outgoing wireless signal to a wireless receiver of a motor unit that is operably associated with the garage door. A wireless signal constructor dynamically constructs the outgoing wireless signal without having access to a secret seed value that is accessible to the motor unit. A local storage unit stores a data-set of rolling codes that are associated with the motor unit; and the outgoing wireless signal is dynamically constructed based on a next-available rolling code obtained from the local storage unit of the base unit.