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

Abstract

The rth generalized Hamming weight d(r) of the Kerdock code of length 2(m) over Z(4) is considered in this correspondence. A lower bound on d(r) is derived for any r, and d(r) is exactly determined for r = 0.5, 1, 1.5, 2, 2.5. In the case of length 2(2m), d(r) is determined for any r, where 0 less than or equal to r less than or equal to m and 2r is an integer. In addition, it is shown that it is sometimes possible to determine the generalized Hamming weights of the Kerdock codes of larger length using the results of d(r) for a given length. This correspondence also provides a closed-form expression for the Lee weight of a Kerdock codeword in terms of the coefficients in its trace expansion.