Cyclically permutable error-correcting codes

In an asynchronous multiplex system a single band of radio frequencies carries many simultaneous conversations, each of which uses a distinguishable train of pulses as a "carrier." To design a good list of allowed pulse trains one is led to a peculiar kind of error-correcting code problem. The encoding sought uses binary -tuples (code words) in which most of the digits are zero. In addition the Hamming distances from any given code word to all cyclic permutations of all other code words must exceed a prescribed minimum value. The code words found herein may be generated simply using a shift register.