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Consider the following code. The legal codewords are those 32-bit sequences in which the number of 1-bits is divisible by 6. That is, a codeword is legal if it is 32-bit long, and of these bits the number of 1-bits is 0, 6, 12, 18, 24, or 30. How much is the Hamming distance of this code, and how many single bit errors can this code detect and correct?

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