Cyclically permutable codes

Abstract: A cyclically permutable code is a set of codewords having the property that no codeword is a cyclic shift of another codeword. We study the problem of constructing cyclically permutable codes of large size and low correlation.Cyclically permutable codes are used in code-division multiple-access systems realized by e.g. direct-sequence modulation or frequency-hopping. Advantages of code-division multiple-access to conventional access methods, such as timedivision and frequency-division, include greater flexibility, better robustness and that no synchronization among the transmitters is needed.Among our main results are an efficient method of selecting cyclically distinct codewords from linear cyclic codes, a new family of sequences for direct-sequence modulation, several constructions of hopping-sequences for multiple-access coupled with a decoding algorithm for asynchronous communication.We have also constructed new binary constant-weight codes of high minimum distance.