Classification of optimal conflict-avoiding codes of weights 6 and 7

A conflict-avoiding code is used to guarantee that each transmitting user can send at least one packet successfully within a fixed period of time, provided that at most k out of M potential users are active simultaneously in a multiple-access collision channel. The number of codewords in a conflict-avoiding code determines the number M of potential users that can be supported in a system. That is why codes of the maximum cardinality for given parameters (optimal codes) are of interest. In this paper we determine the values of the maximum cardinality and classify up to multiplier equivalence optimal conflict-avoiding codes for 6 and 7 active users and given small lengths.