What should be the minimum hamming distance dmin to guarantee correction of upto p errors in a given block code.
Explanation
The Mathematical Requirement
For a decoder to successfully map a corrupted message back to the correct original codeword, the received signal must fall within the unique radius of that codeword.
If we want to correct up to p errors:
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Each codeword gets a "sphere" of radius p.
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To prevent these spheres from overlapping, the distance between the centers (the codewords) must be more than the sum of the two radii (p+p).
Therefore:
Since the Hamming distance must be an integer, the next possible value is:
