On a Particular Class of Minihypers and Its Applications. I. The Result for General q

This article is the first in a series of three articles that discuss a particular class of minihypers and its applications. Proving that for small and < N, a {v _{+ 1}, v ; N, q}-minihyper consists of a sum of -spaces, we show that the excess points of an s-cover with excess of PG(N, q), (s + 1)|(N + 1), form a sum of s-spaces, and that no maximal partial s-spreads with deficiency of PG(N, q), (s + 1)|(N + 1), exist. The case q square will be studied in greater detail in 7] and further applications of these classification results on this class of minihypers will be published in 8].