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Recently, active research has been performed on constructing t-designs from linear codes over Z4. In this paper, we will construct a new simple 3 − (2m, 7, 14/3 (2m − 8)) design from codewords of Hamming weight 7 in the Z4-Goethals code for odd m ≥ 5. For 3 arbitrary positions, we will count the number of codewords of Hamming weight 7 whose support includes those 3 positions. This counting can...
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