Which method is used for both error detection and error correction method in…

A method achieves error detection when it can notice that a received code word does not match any valid transmitted word. It achieves error correction only when it can go one step further and pinpoint exactly which bit changed. That pinpointing is possible only when valid code words are spaced apart by a large-enough minimum Hamming Distance (dmin), so a corrupted word still lands closer to one specific valid word than to any other.

Here, maintaining dmin = 3 between valid code words is exactly what lets a Hamming-code-based system both detect up to 2-bit errors and correct a 1-bit error — because at that distance, at most one valid code word can be within 1 bit of the received word. That dual detect-and-correct property is what the question is testing, and it is why Hamming Distance is the correct choice here.

By contrast, the other methods offered are detection-only:

• Single Parity Check — can only flag that an odd number of bits flipped; it carries no positional information, so it cannot correct.

• Cyclic Redundancy Check (CRC) — a strong detector via polynomial division, but standard networking protocols (e.g. Ethernet) use it purely to flag corruption; a frame that fails the check is discarded, not repaired.

• Checksum — also detection-only (used in IP/TCP/UDP headers); cheap to compute but structurally unable to localize a specific bit error.

Note the distinction the question is probing: Hamming Code is the actual bit-pattern scheme built on top of this idea, while Hamming Distance is the underlying metric that gives that scheme its detect-and-correct power. “Hamming Code” is not one of the four choices offered here — among Single Parity Check, Hamming Distance, CRC, and Checksum, Hamming Distance is the one that captures this dual capability.