In Hamming Code, the relationship between the distance between parity bits and their error detection and correction capability is crucial. The distance between parity bits is known as Hamming distance.

1. Hamming Distance: This is the number of bit positions in which two codewords differ. In error detection and correction, the Hamming distance is used to determine the minimum number of changes required to go from one valid codeword to another.

2. Error Detection: If the Hamming distance between valid codewords is D, then it can detect up to D-1 errors. This is because if less than D-1 errors occur, the received codeword will be closer to the original valid codeword than any other valid codeword, allowing the detection of the error.

3. Error Correction: If the Hamming distance between valid codewords is D, then it can correct up to (D-1)/2 errors. This is because if (D-1)/2 or fewer errors occur, the received codeword will be closer to the original valid codeword than any other valid codeword, allowing the correction of the error.

So, in conclusion, the greater the distance between parity bits (i.e., the greater the Hamming distance), the higher the error detection and correction capability.

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In Hamming Code, the relationship between the distance between parity bits and their error detection and correction capability is crucial. The distance between parity bits is known as Hamming distance.

1. Hamming Distance: This is the number of bit positions in which two codewords differ. In error detection and correction, the Hamming distance is used to determine the minimum number of changes required to go from one valid codeword to another.

2. Error Detection: If the Hamming distance between valid codewords is D, then it can detect up to D-1 errors. This is because if less than D-1 errors occur, the received codeword will be closer to the original valid codeword than any other valid codeword, allowing the detection of the error.

3. Error Correction: If the Hamming distance between valid codewords is D, then it can correct up to (D-1)/2 errors. This is because if (D-1)/2 or fewer errors occur, the received codeword will be closer to the original valid codeword than any other valid codeword, allowing the correction of the error.

So, in conclusion, the greater the distance between parity bits (i.e., the greater the Hamming distance), the higher the error detection and correction capability.

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In Hamming Code, the relationship between the distance between parity bits and their error detection and correction capability is crucial. The distance between parity bits is known as Hamming distance.

1. Hamming Distance: This is the number of bit positions in which two codewords differ. In error detection and correction, the Hamming distance is used to determine the minimum number of changes required to go from one valid codeword to another.

2. Error Detection: If the Hamming distance between valid codewords is D, then it can detect up to D-1 errors. This is because if less than D-1 errors occur, the received codeword will be closer to the original valid codeword than any other valid codeword, allowing the detection of the error.

3. Error Correction: If the Hamming distance between valid codewords is D, then it can correct up to (D-1)/2 errors. This is because if (D-1)/2 or fewer errors occur, the received codeword will be closer to the original valid codeword than any other valid codeword, allowing the correction of the error.

So, in conclusion, the greater the distance between parity bits (i.e., the greater the Hamming distance), the higher the error detection and correction capability.

What is the relationship between the distance between parity bits and their error detection and correction capability in Hamming Code?Closer parity bits provide higher error correction capabilityCloser parity bits provide lower error correction capabilityDistance between parity

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