  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 $L=pq$.
