generatorToParityCheck -- parity check matrix of a linear code

i1 : F = GF 2;

i2 : L = {{0,1,1,0},{1,0,1,0},{0,0,0,1}};

i3 : G = matrix apply(L, codeword->apply(codeword, en -> sub(en,F)))

o3 = | 0 1 1 0 |
     | 1 0 1 0 |
     | 0 0 0 1 |

             3      4
o3 : Matrix F  <-- F

i4 : H = generatorToParityCheck G

o4 = | 1 1 1 0 |

             1      4
o4 : Matrix F  <-- F

i5 : K = GF(8,Variable => a);

i6 : G = matrix {{1,0,0,a,0,1,1,a},{0,0,0,1,1,1,1,0},{1,1,0,0,0,1,0,0},{1,0,1,0,0,1,1,0}}

o6 = | 1 0 0 a 0 1 1 a |
     | 0 0 0 1 1 1 1 0 |
     | 1 1 0 0 0 1 0 0 |
     | 1 0 1 0 0 1 1 0 |

             4      8
o6 : Matrix K  <-- K

i7 : H = generatorToParityCheck G

o7 = | 1 0 0 0 1 1 0 0    |
     | 0 1 0 0 0 1 1 0    |
     | 0 0 1 0 1 0 1 a2+1 |
     | 0 0 0 1 1 0 0 1    |

             4      8
o7 : Matrix K  <-- K