This preprint was accepted August 28, 1998
Contact: M. M. Skriganov
ABSTRACT: In the present paper we consider finite point sets of a special kind, $q$-optimum distributions, which fill out the $n$-dimensional unit cube very uniformly. It turns out that such point sets have a rather rich combinatorial structure, namely, we show that $q$-optimum distributions can be characterized as maximum distance codes with respect to a non-Hamming metric. Broad classes of such codes and distributions are explicity constructed by Hermite interpolations over finite fields. In addition, weight spectra of maximum distance codes are also evaluated precisely in the paper.