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Petersburg Department of Steklov Institute of Mathematics

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PREPRINT 16/1998

M. M. Skriganov
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ERROR-CORRECTING CODES,
AND INTERPOLATIONS OVER FINITE FIELDS

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.

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