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Stevesand85 (talk | contribs) →Decoding: y is not necessarily a codeword at the beginning of the algorithm, it's just an n-dimensional word in general. |
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Let <math>v_i\,</math> be the vertex of <math>L\,</math> that corresponds to the <math>i\,</math>th index in the codewords of <math>C\,</math>. Let <math>y \in \{0,1\}^n\,</math> be a received word, and <math>V(y) = \{v_i | \text{ the } i^{\text{th}} \text{ position of } y \text{ is a } 1\}\,</math>. Let <math>e(i)\,</math> be <math>|\{v \in R | N(v) \cap V(y)\,</math> is even<math>\}|\,</math>, and <math>o(i)\,</math> be <math>|\{v \in R | N(v) \cap V(y) \,</math> is odd<math>\}|\,</math>. Then consider the greedy algorithm:
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'''Input:''' received
initialize y' to y
while there is a v in R adjacent to an odd number of vertices in V(y')
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