How many binary words are there

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Reference no: EM131349957

Let n = 2^r-1, and consider a binary word of block length n. How many binary words are there that differ from the given word in not more than one place? Given 2^k distinct binary words of block length n with the property that any one of the words with one bit changed differs from every other word in at least two bit positions, how big can k be? Prove that no binary single-error-correcting code can have fewer check symbols than the Hamming code.

Reference no: EM131349957

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