  In this paper we construct multidimensional codes with high dimension. The
codes can correct high dimensional errors which have the form of either small
clusters, or confined to an area with a small radius. We also consider small
number of errors in a small area. The clusters which are discussed are mainly
spheres such as semi-crosses and crosses. Also considered are clusters with
small number of errors such as 2-bursts, two errors in various clusters, and
three errors on a line. Our main focus is on the redundancy of the codes when
the most dominant parameter is the dimension of the code.
