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Theorem 8.5 Let dmin be the minimum distance for a group code C.Then dmin is the minimum of all the nonzero weights of the nonzero codewords in C.That is, dmin=min{w(x):x≠O}. PROOF.Observe that dmin=min{d(x,y):x≠y} =min{d(x,y):x+y≠0} =mim{w(X+y):X+y丰0今 这是为什么? =min{w(z):z≠0}. We have now reduced the problem of finding "good"codes to that of generating group codes.这是为什么?
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