Web Reference: May 19, 2025 · Error-correcting codes are mathematical constructs designed to optimize the transmission of data over unreliable or noise-infused channels. By adding redundant information to messages, the receiver can detect, and sometimes correct, any errors introduced during transmission. In the age of information technology, error-correcting codes are widely used in communication systems and data storage systems. Both types of systems share the same model, as shown in Fig 1. Hamming code encodes 4 bits (x1; x2; x3; x4) as (x1; x2; x3; x4; a; b; c), where a = x2 + x3 + x4, b = x1 + x3 + x4 and c = x1 + x2 + x4. It has block-size 7, dimension 4 and distance 3. Think: Their generator matrix? (C) equals the minimum number of columns of H that are linearly dependent.
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