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Linear codes and error correction
Minimum distance, detection, and correction

28. Linear codes and error correction

Minimum distance, detection, and correction

Level: avanzado

In 28. Linear codes and error correction

Formula

d_{\min} = \min_{\mathbf c_1\neq\mathbf c_2} d_H(\mathbf c_1,\mathbf c_2).

Equivalent form

d_{\min}-1

Equivalent form

t = \left\lfloor \frac{d_{\min}-1}{2} \right\rfloor

For a linear code

d_{\min} = \min_{\mathbf c\neq\mathbf0}w_H(\mathbf c).

Tags

algebra
codes
linear codes
CS
algebra formula

Detail

The separation between codewords determines the theoretical detection and correction capability.

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