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On the weight hierarchy of Kerdock codes over Z4

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4 Author(s)
Kyeongcheol Yang ; Dept. of Electron. Commun. Eng., Hanyang Univ., Seoul, South Korea ; Helleseth, T. ; Kumar, P.V. ; Shanbhag, A.G.

The rth generalized Hamming weight dr of the Kerdock code of length 2m over Z4 is considered. A lower bound on dr is derived for any r, and dr is exactly determined for r=0.5, 1, 1.5, 2, 2.5. In the case of length 2 2m, dr 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 dr 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

Published in:

Information Theory, IEEE Transactions on  (Volume:42 ,  Issue: 5 )

Date of Publication:

Sep 1996

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