On the weight hierarchy of Kerdock codes over Z4

The rth generalized Hamming weight d_r of the Kerdock code of length 2^m over Z₄ is considered. 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⩽r⩽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. The authors also provide a closed-form expression for the Lee weight of a Kerdock codeword in terms of the coefficients in its trace expansion