This paper presents a scheme named code hopping (CodeHop) for gaussian wiretap channels based on nonsystematic low-density parity-check (LDPC) codes. Different from traditional communications, in the CodeHop scheme, the legitimate receiver (Bob) rapidly switches the parity-check matrix upon each correctly received source message block. Given an authenticated public feedback channel, the transmitter's (Alice) parity-check matrix can also be synchronized with the receiver's. As a result, once an eavesdropper (Eve) erroneously decodes a message block, she may not be able to follow the update of subsequent parity-check matrices. Thus, the average BER of Eve will be very close to $0.5$ if the transmitted number of message blocks is large enough. Focused on the measure of security gap defined as the difference of channel quality between Bob and Eve, numerical results show that the CodeHop scheme outperforms other solutions by sufficiently reducing the security gap without sacrificing the error-correcting performance of Bob.