  In a frequency hopping (FH) scheme users communicate simultaneously using FH
sequences defined on the same set of frequency channels. An FH sequence
specifies the frequency channel to be used as communication progresses. Much of
the research on the performance of FH schemes is based on either pairwise
mutual interference or adversarial interference but not both. In this paper, we
evaluate the performance of an FH scheme with respect to both group-wise mutual
interference and adversarial interference (jamming), bearing in mind that more
than two users may be transmitting simultaneously in the presence of a jammer.
We establish a correspondence between a cover-free code and an FH scheme. This
gives a lower bound on the transmission capacity. Furthermore, we specify a
jammer model and consider what additional properties a cover-free code should
have to resist the jammer. We demonstrate that a purely combinatorial approach
is inadequate against such a jammer, but that with the use of pseudorandomness,
we can have a system that has high throughput as well as security against
jamming.
