Binary [32,2,21] Goppa code
First construction:
Goppa polynomial: G(z)=z8+z6+z5+z4+z3+z2+1
Field used: GF(25)
L=GF(25) ∪ {0}
The field GF(25) is constructed using the primitive polynomial p(x)=x5+x2+1, p(α)=0;
Second construction:
Goppa polynomial: G(z)=z5+z2+1
Field used: GF(210)
L={γi | i=0,1, ... 32}
γ=α31
The field GF(210) is constructed using the primitive polynomial p(x)=x10+x3+1, p(α)=0;
Note: The length is one less than 33=|L| used above, because in the generation of the H-Matrix a column gets zero.