ON THE WEIGHT HIERARCHY OF GOETHALS CODES OVER Z(4)

Abstract

The rth generalized Hamming weight d(r)(m,j) of the Goethals code g(m)(j) of length 2(m) over Z(4) is considered in this correspondence. Zn the case that m greater than or equal to 3 is an odd integer, d(r)(m,j) is exactly determined for r = 0.51 1, 1.5, 2, 2.5, and 3.0. For a composite m, we give an upper bound d(r)(m,j) using the lifting technique.