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Suppose n = 10. Is there some finite alphabet Q such that there are vectors x,...

Suppose n = 10. Is there some finite alphabet Q such that there are vectors x, y, z, and w in Q^n (i.e., q-ary n-tuples, with q the size of Q) such that (with d denoting Hamming distance) d(x,y) = 4, d(x,z) = 8, d(x,w) = 5, d(y,z) = 3, d(y,w) = 4, and d(z,w) = 3 ? (Hamming Distance)

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