A study of -minihypers in

We study ( x v t , x v t − 1 ) -minihypers in PG ( t , q ) , i.e. minihypers with the same parameters as a weighted sum of x hyperplanes. We characterize these minihypers as a nonnegative rational sum of hyperplanes and we use this characterization to extend and improve the main results of several papers which have appeared on the special case t = 2 . We establish a new link with coding theory and we use this link to construct several new infinite classes of ( x v t , x v t − 1 ) -minihypers in PG ( t , q ) that cannot be written as an integer sum of hyperplanes.