On the weight hierarchy of Preparata codes over Z(4)
Recently, Hammons et al. showed that, when properly defined, the binary nonlinear Preparata code can be considered as the Gray map of a linear code over Z(4), the so-called Preparata code over Z(4). In this paper, we consider the rth generalized Hamming weight d(r)(m) of the Preparata code of length 2(m) over Z(4). For any m greater than or equal to 3, d(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(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 = T, the weight hierarchy is completely determined except for d(4)(7).
weight hierarchy preparata codes linear codes over z(4) generalized hamming weights kerdock codes minimum support size nonlinear codes