A tight asymptotic bound on the size of constant-weight conflict-avoiding codes

In the study of multiple-access in the collision channel, conflict-avoiding code is used to guarantee that each transmitting user can send at least one packet successfully in the worst case within a fixed period of time, provided that at most k users out of M potential users are active simultaneously. The number of codewords in a conflict-avoiding code determines the number of potential users that can be supported in a system. Previously, upper bound on the size of conflict-avoiding code is known only for Hamming weights three, four and five. The asymptotic upper in this paper extends the known results to all Hamming weights, and is proved to be tight by exhibiting infinite sequences of conflict-avoiding codes which meet this bound asymptotically for all Hamming weights.