Which code is a simple linear block code commonly used for error detection and correction in small data blocks?

Which code is a simple linear block code commonly used for error detection and correction in small data blocks?

• A. Hamming code
• B. Reed-Solomon code
• C. Convolutional code
• D. Shannon limit

Answer: (A)

Hamming codes are simple linear block codes that add a few parity bits to a small data block so the receiver can pinpoint and fix a single-bit error. The parity bits are placed at positions that are powers of two, and when the codeword is checked, a syndrome value points to the exact bit that is in error, allowing it to be flipped back to the correct value. Because of this straightforward syndrome-based decoding, they work well for small messages where keeping overhead low matters. In contrast, Reed-Solomon codes operate on symbols and handle larger blocks with many errors, and are more suited to burst error environments like CDs, DVDs, or QR codes. Convolutional codes are designed for continuous data streams with memory, decoded with procedures like the Viterbi algorithm, not fixed-size blocks. The Shannon limit is a theoretical bound on how much information can be transmitted reliably, not a specific code. So the simplest linear block code commonly used for error detection and correction in small data blocks is the Hamming code.

Hamming codes are simple linear block codes that add a few parity bits to a small data block so the receiver can pinpoint and fix a single-bit error. The parity bits are placed at positions that are powers of two, and when the codeword is checked, a syndrome value points to the exact bit that is in error, allowing it to be flipped back to the correct value. Because of this straightforward syndrome-based decoding, they work well for small messages where keeping overhead low matters. In contrast, Reed-Solomon codes operate on symbols and handle larger blocks with many errors, and are more suited to burst error environments like CDs, DVDs, or QR codes. Convolutional codes are designed for continuous data streams with memory, decoded with procedures like the Viterbi algorithm, not fixed-size blocks. The Shannon limit is a theoretical bound on how much information can be transmitted reliably, not a specific code. So the simplest linear block code commonly used for error detection and correction in small data blocks is the Hamming code.