A new reducibility result for minihypers in finite projective geometries

In this paper, we prove a new reducibility result for minihypers in projective geometries over finite fields. It is further used to characterize the minihypers with parameters $(70,22)$ in $PG(4,3)$. The latter can be used to attack the existence problem for some hypothetical ternary Griesmer codes of dimension 6.