Consider the vector space V 23 and the Golay code subspace C23, 12 Prove that there are (a) 2 23 vectors in V23 (b) 4096 vectors in C2312 c) 2048 vectors in each sphere of radius 3 about a vector in C 2312 , (given that each element of V 23 is in one sphere). How many vectors of distance 1, 2, and 3 are in each sphere of radius 3?

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