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Algebra
Linear codes and error correction
Hamming distance and weight

28. Linear codes and error correction

Hamming distance and weight

Level: avanzado

In 28. Linear codes and error correction

Formula

d_H(\mathbf x,\mathbf y) = |\{i:x_i\neq y_i\}|.

Equivalent form

w_H(\mathbf x) = d_H(\mathbf x,\mathbf0).

Tags

algebra
codes
linear codes
CS
algebra formula

Detail

Counts how many positions differ between two words.

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Minimum distance, detection, and correction
$d_{\min} = \min_{\mathbf c_1\neq\mathbf c_2} d_H(\mathbf c_1,\mathbf c_2).$
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