Abstract: A trainable transceiver for learning and transmitting an activation signal that includes a rolling or other variable code for remotely actuating a device, such as a garage door opener. The trainable transceiver preferably includes a receiver, a signal generator, and a controller operating in a learning mode or in an operating mode. In the learning mode the controller recognizes the presence of a variable code, identifies a prestored cryptographic algorithm related to the cryptographic algorithm used by the remote transmitter to generate the variable code, and stores data identifying the cryptographic algorithm and last transmitted code of the activation signal. In the operating mode, the controller generates output data representing a next sequential code of the variable code using the identified cryptographic algorithm and the data representing the last transmitted code.