  Let $\mathbb{F}_p$ be the prime field of order $p>0$ and $G$ be an elementary
abelian $p$-group.For some $n$-dimensional cohyperplane $G$-representations $V$
over $\mathbb{F}_p$, we show that $\mathbb{F}_p[V\oplus V^*]^G$, the invariant
ring of a vector and a covector is a complete intersection by exhibiting an
explicit generating set (in fact, a SAGBI basis) and exposing all relations
among the generators.
