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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 \left| \sum_{i=0}^{n-1} \frac{c_i}{x-L_i} \equiv 0 \mod g(x) \right. \right\}</math>
Code defined by a tuple <math>(g,L)</math> has minimum distance <math>2t+1</math>, thus it can correct <math>t=\left\lfloor \frac{(2t+1)-1}{2} \right\rfloor</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
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