On the weight hierarchy of Kerdock codes over Z/sub 4/
Kyeongcheol Yang, Tor Helleseth, P. Vijay Kumar, A.G. Shanbhag · IEEE Transactions on Information Theory · 1996
The rth generalized Hamming weight d/sub r/ of the Kerdock code of length 2/sup m/ over Z/sub 4/ is considered. A lower bound on d/sub r/ is derived for any r, and d/sub r/ is exactly determined for r=0.5, 1, 1.5, 2, 2.5. In the case of length 2/sup 2m/, d/sub r/ is determined for any r, where 0/spl les/r/spl les/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/sub 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.