Solution:

The minimum Hamming distance of a block code, denoted as d_{min}, determines its error-detecting and error-correcting capability.

- To detect up to p errors, the minimum distance must satisfy: d_{min} \geq p + 1.

- To correct up to p errors, the minimum distance must satisfy: d_{min} \geq 2p + 1.

This is because with distance 2p + 1, the codewords are far enough apart that even if p errors occur, the received word is still closer to the correct codeword than to any other.

✅ Correct Answer: (B) 2p + 1