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Hello, I was struggling with Hamming Code and I think I now have a good understanding of Hamming Correction but I just want to make sure it's correct.
When we look at a codeword that has been encoded using the Hamming Code, it is a general rule that a parity bit will always be in the position that is a power of 2. Meaning that a parity bit is correlated to data bits that, when broken down into a sum of powers of 2, one of their addends is equal to that parity bit's position.
This implies that we are working with the highest possible power of 2 downwards. For example, if we look at a data bit that is in position 10, the highest possible power of 2 that fits in 10 is 8. Then we are left with 2. So this data bit contributes to parity bits in positions 2 and 8.
If the sender encoded using even parity, then the receiver must also check for errors in even parity. So if Parity Bit 1 is related to data bits 3, 5, 7, 9, 11, where, including the value of the parity bit, there is an odd number of 1's among these 6 values, that means that there is an error and c+=1 where 1 is the position of the parity bit. Then we work out the other parity bits in the same way.
Is this correct?