Binary Goppa code: Difference between revisions

Revision as of 13:50, 31 December 2012

Revision as of 13:51, 31 December 2012

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Codewords belong to the kernel of syndrome function, forming a subspace of <math>\{0,1\}^n</math>:

: <math>\Gamma(g,L)=\left\{ c \in \{0,1\}^n | \sumsum_{i=0}^{n-1} \frac{c_i}{x-L_i} \equiv 0 \mod g(x) \right\}</math>

Code defined by a tuple <math>(g,L)</math> has minimum distance <math>2t-1</math>, thus it can correct <math>t</math> errors in a word of size <math>n-mt</math> using codewords of size <math>n</math>. It also possesses a convenient [[parity-check matrix]] <math>H</math> in form