Constructions for optimal constant weight cyclically permutable codes and difference families

A cyclically permutable code is a binary code whose codewords are cyclically distinct and have full cyclic order. An important class of these codes are the constant weight cyclically permutable codes. In a code of this class all codewords have the same weight w. These codes have wide applications, e.g., in optical code-division multiple access communication systems and in constructing protocol-sequence sets for the M-active-out-of-T users collision channel without feedback. In this paper we construct optimal constant weight cyclically permutable codes with length n, weight w, and minimum Hamming distance 2w-2. Some of these codes coincide with the well known design called difference family