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On the weight hierarchy of Preparata codes over Z4

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2 Author(s)
Kyeongcheol Yang ; Dept. of Electron. Commun. Eng., Hanyang Univ., Seoul, South Korea ; Helleseth, T.

Hammons et al. (see ibid., vol.40, p.301-19, 1994) showed that, when properly defined, the binary nonlinear Preparata code can be considered as the Gray map of a linear code over Z4, the so called Preparata code over Z4. We consider the rth generalized Hamming weight dr(m) of the Preparata code of length 2m over Z4. For any m⩾3, dr(m) is exactly determined for r=0.5, 1, 1.5, 2, 2.5 and 3.0. For a composite m, we give an upper bound on dr(m) using the lifting technique. For m=3, 4, 5, 6 and 8, the weight hierarchy is completely determined. In the case of m=7, the weight hierarchy is completely determined except for d4(7)

Published in:

Information Theory, IEEE Transactions on  (Volume:43 ,  Issue: 6 )

Date of Publication:

Nov 1997

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