Intersection sets, three-character multisets and associated codes.

In this article we construct new minimal intersection sets in AG(r, q^2 ) sporting
three intersection numbers with hyperplanes; we then use these sets to obtain linear error cor-
recting codes with few weights, whose weight enumerator we also determine. Furthermore,
we provide a new family of three-character multisets in PG(r, q^2 ) with r even and we also
compute their weight distribution.