Split weight enumerators for the preparata codes with applications to designs

Abstract

For quaternary Preparata and Kerdock codes of length N=2(m), m odd, we prove that the split complete weight enumerator for a coordinate partition into 3 and N-3 coordinates is independent of the chosen partition. The result implies that the words of a given complete weight in either a Preparata code or Kerdock code define a 3-design.