A new upper bound and optimal constructions of equi-difference conflict-avoiding codes on constant weight.

Conflict-avoiding codes (CACs) have been used in multiple-access collision channel without feedback. The size of a CAC is the number of potential users that can be supported in the system. A code with maximum size is called optimal. The use of an optimal CAC enables the largest possible number of asynchronous users to transmit information efficiently and reliably. In this paper, a new upper bound on the maximum size of arbitrary equi-difference CAC is presented. Furthermore, three optimal constructions of equi-difference CACs are also given. One is a generalized construction for prime length $L=p$ and the other two are for two-prime length $L=pq$.