On a Particular Class of Minihypers and Its Applications: II. Improvements for q Square

A particular class of minihypers was studied previously by the authors (in press, Des. Codes Cryptogr.). For q square, this paper improves the results of that work, under the assumption that no weights occur in the minihyper. Using the link between these minihypers and maximal partial s-spreads of PG(N, q), (s+1) ∣ (N+1), the findings on minihypers translate immediately into results on the extendability of partial s-spreads with small positive deficiency. Other applications of this characterisation of minihypers are given by P. Govaerts et al. (in press, European J. Combin.).