Onto, and one-to-one functions Hamming distance In computer science, the hamming distance (named after Richard Hamming)...

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Onto, and one-to-one functions Hamming distance In computer science, the hamming distance (named after Richard Hamming) is a function used to count the number of flipped bits in a fixed-length binary lists. It is used in error correction and detection in information theory and other applications. Let's define the Hamming distance function H between two binary lists of size 6. H: {0, 1}6 × {0, 1}6 → NU {0} defined for any two binary lists of size 6 by: H (11, 12) = the number of positions where ₁ and 12 differ We will simplify writing lists in {0, 1}6 by removing the parentheses and the commas. For example, the list (0,0,0,0,0,1) will be written as 000001. 1. Calculate H(000010, 000011), and H (000010, 100001). 2. Prove that H is not onto. 3. Prove that H is not one-to-one. 4. Propose a change in the domain of H to make the function onto. Onto, and one-to-one functions Hamming distance In computer science, the hamming distance (named after Richard Hamming) is a function used to count the number of flipped bits in a fixed-length binary lists. It is used in error correction and detection in information theory and other applications. Let's define the Hamming distance function H between two binary lists of size 6. H: {0, 1}6 × {0, 1}6 → NU {0} defined for any two binary lists of size 6 by: H (11, 12) = the number of positions where ₁ and 12 differ We will simplify writing lists in {0, 1}6 by removing the parentheses and the commas. For example, the list (0,0,0,0,0,1) will be written as 000001. 1. Calculate H(000010, 000011), and H (000010, 100001). 2. Prove that H is not onto. 3. Prove that H is not one-to-one. 4. Propose a change in the domain of H to make the function onto.