On Optical Orthogonal, Cyclically Permutable, and Super Optical Orthogonal Codes

Optical orthogonal codes (OOC) are special classes of codes for applications in code division multi-access (CDMA) transmission using an optical carrier. We show a new relationship between constant weight cyclically permutable codes (CPC) and OOC´s which can be investigated further. The main result ties together the CPC´s and the solution of an algebraic system of congruences. For a particular case, there is a recurrence relationship for the code cardinality. More general cases need to be elaborated in coming research. We discuss also so-called super OOC´s, which are codes with stronger correlation properties, and show several examples of such codes derivable from CPC´s designed by applying the method proposed.