On the weight hierarchy of Preparata codes over Z/sub 4/

Abstract

Hammons et al. (see ibid., vol.40, p.301-19, 1994) showed that, when properly defined, the binary nonlinear Preparata code can be considered as the Gray map of a linear code over Z/sub 4/, the so called Preparata code over Z/sub 4/. We consider the rth generalized Hamming weight d/sub r/(m) of the Preparata code of length 2/sup m/ over Z/sub 4/. For any m/spl ges/3, d/sub r/(m) is exactly determined for r=0.5, 1, 1.5, 2, 2.5 and 3.0. For a composite m, we give an upper bound on d/sub r/(m) using the lifting technique. For m=3, 4, 5, 6 and 8, the weight hierarchy is completely determined. In the case of m=7, the weight hierarchy is completely determined except for d/sub 4/(7).