Weight distribution of Preparata codes over Z
4 and the construction of 3-designs |
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| Authors: | WeiXia Li Hao Shen |
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| Institution: | 1. School of Mathematical Sciences, Qingdao University, Qingdao, 266071, China
2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China
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| Abstract: | In this paper, we calculate the number of the codewords (with Hamming weight 7) of each type in the Preparata codes over Z 4, then give the parameter sets of 3-designs constructed from the supports of the codewords of each type. Moreover, we prove that the first two families of 3-designs are simple and the third family of the 3-designs has repeated blocks. |
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| Keywords: | t-designs weight distribution Preparata codes over Z |
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