Further results on generalized Hamming weights for Goethals and Preparata codes over Z(4)
This correspondence contains results on the generalized Hamming weights (GHW) for the Goethals and Preparata codes over Z(4). We give an upper bound on the rth generalized Hamming weights d(r)(m, j) for the Goethals code G(m)(j) of length 2(m) over Z(4), when nz is odd. We also determine d(3.5)(m,j) exactly. The upper bound is shown to be tight up to r = 3.5. Furthermore, we determine the rth generalized Hamming weight d(r)(m) for the Preparata code of length 2(m) over Z(4) when r = 3.5 and r = 4.
generalized hamming weights preparata codes goethals codes linear codes over z(4) minimum support size nonlinear code weight hierarchy