Intersection sets,three-character multisets and associated codes

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