Title: Blocks with the hyperfocal subgroup $Z_{2^n}\times Z_{2^n}$,
Abstract: In this paper, we calculate the numbers of irreducible ordinary characters
and irreducible Brauer characters in a block of a finite group $G$, whose
associated fusion system over a 2-subgroup $P$ of $G$ (which is a defect group
of the block) has the hyperfocal subgroup $\mathbb Z_{2^n}\times \mathbb
Z_{2^n}$ for some $n\geq 2$, when the block is controlled by the normalizer
$N_G(P)$ and the hyperfocal subgroup is contained in the center of $P$, or when
the block is not controlled by $N_G(P)$ and the hyperfocal subgroup is
contained in the center of the unique essential subgroup in the fusion system.
In particular, Alperin's weight conjecture holds in the considered cases.