A discrete isodiametric result: The Erdős–Ko–Rado theorem for multisets

There are many generalizations of the Erdős–Ko–Rado theorem. Here the new results (and problems) concern families of tt-intersecting kk-element multisets of an nn-set. We point out connections to coding theory and geometry. We verify the conjecture that for n≥t(k−t)+2n≥t(k−t)+2 such a family can have at most (n+k−t−1k−t) members.