Repeated use of codes for error detection five times is bad

The undetected error probabilities of codes when used repeatedly to transmit sequences of messages are studied. It is shown that for any code whose rate is greater than zero but less than one, the coding scheme obtained by the repeated use of the code is bad, if used five times or more, and improper if used four times or more. Furthermore, the repeated use of any linear code, over an alphabet greater than five, more than once, is bad and improper.