The rows of a permutation array form an error-correcting code with minimum distance $s-\lambda$. Codes formed in this manner, called [*permutation codes*]{}, have more recently attracted attention due to their applications to powerline communications; see [@ChuColbournDukes; @ColbournKloveLing; @Huczynska]. In [@DezaVanstone], it is noted that a $2$-${\mathrm{GHD}}_k(s,v;\lambda)$ is equivalent to a $k$-uniform $\mathrm{PA}(s,\lambda;v)$. In the case that $s=\frac{\lambda(v-1)}{k-1}$, so that the ${\mathrm{GHD}}$ is a doubly resolvable BIBD, the permutation array is equidistant.

There are also known connections between GHDs and other classes of codes. A [*doubly constant weight code*]{} is a binary constant-weight code with length $n=n_1+n_2$ and weight $w=w_1+w_2$, where each codeword has $w_1$ 1s in the first $n_1$ positions and $w_2$ 1s in the final $n_2$ positions. Such a code with minimum distance $d$ is referred to as a $(w_1,n_1,w_2,n_2,d)$-code. In [@Etzion], Etzion describes connections between certain classes of designs and optimal doubly constant weight codes. In particular, a $2$-${\mathrm{GHD}}_k(s,v;1)$ gives a $(2,2s,k,v,2k+2)$-code.

GHDs as generalized packing designs
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The notion of [*generalized $t$-designs*]{} introduced by Cameron in 2009 [@Cameron09], and the broader notion of [*generalized packing designs*]{} introduced by Bailey and Burgess [@packings], provide a common framework for studying many classes of combinatorial designs. As described below, generalized 