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: <math>\forall i,j \in \mathbb{Z}_n: L_i \in GF(2^m) \and L_i \neq L_j \and g(L_i) \neq 0</math>
Codewords belong to the kernel of syndrome function, forming a subspace of <math>\{0,1\}^n</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 possesses a [[parity-check matrix]] <math>H</math> in form▼
: <math>\Gamma(g,L)=\left\{ c \in \{0,1\}^n | \sum \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
: <math>
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