On the weight hierarchy of Preparata codes over Z4 |
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Authors: | Kyeongcheol Yang Helleseth T |
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Affiliation: | Dept. of Electron. Commun. Eng., Hanyang Univ., Seoul; |
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Abstract: | 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) |
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