Further Results on Generalized Hamming Weights for Goethals and Preparata Codes Over Z4

This paper contains results on the generalized Hamming weights 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 m 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: