New Results on Optimal Multichannel Conflict-Avoiding Codes

A multichannel conflict-avoiding code of length
$L$
and weight
$w$
for
$M$
orthogonal channels, denoted by MC-CAC(M, L, w), is used for deterministic multiple-access without feedback. When the number of simultaneously active users is less than or equal to w, an MC-CAC(M, L, w) is able to provide a hard guarantee that each active user has a successful transmission within every consecutive
$L$
time slots. An upper bound on the number of potential users, or codewords, that an MC-CAC(2, L, 3) can support is derived in this paper. By means of (hooked) Skolem sequences, we propose a new construction that can provide a series of optimal MC-CAC(2, L, 3)s in the sense that the code sizes achieve the obtained upper bounds.