Home/Algebra/Linear codes and error correction/Generator matrix28. Linear codes and error correctionGenerator matrixLevel: avanzadoIn 28. Linear codes and error correctionFormulaCopy LaTeXG∈Fqk×n.G\in\mathbb F_q^{k\times n}.G∈Fqk×n.Equivalent formCopy LaTeXc=mG.\mathbf c=\mathbf mG.c=mG.Tagsalgebracodeslinear codesCSalgebra formulaDetailConverts a message of kkk symbols into a codeword of nnn symbols.Explore the ideaComputational complexityShow (CS mode)Found an error? Contact us.Related formulasRelatedMatrix product(AB)ij=∑kaikbkj(AB)_{ij}=\sum_k a_{ik}b_{kj}(AB)ij=k∑aikbkjOpen formulaOpen in sectionRelatedPrime finite fieldFp=Z/pZ(p primo)\mathbb F_p=\mathbb Z/p\mathbb Z\quad(p\text{ primo})Fp=Z/pZ(p primo)Open formulaOpen in sectionRelatedLinear code over a finite fieldC≤Fqn.C\le \mathbb F_q^n.C≤Fqn.Open formulaOpen in sectionRelatedParity-check matrixHcT=0.H\mathbf c^T=\mathbf0.HcT=0.Open formulaOpen in section