Partial permutation decoding for MacDonald codes

We show how to find s-PD-sets of the minimal size (s+1) for the (left[ frac{q^n-q^u}{q-1},n,q^{n-1}-q^{u-1}right] _q ) MacDonald q-ary codes (C_{n,u}(q)) where (n ge 3) and (1 le u le n-1). The construction of [6] can be used and gives s-PD-sets for s up to the bound (lfloor frac{q^{n-u}-1}{(n-u)(q-1)} rfloor -1), of effective use for u small; for (u ge lfloor frac{n}{2} rfloor ) an alternative construction is given that applies up to a bound that depends on the maximum size of a set of vectors in (V_u(mathbb {F}_q)) with each pair of vectors distance at least 3 apart.