Binary [56,16,20] Goppa code
Goppa polynomial: G(z)=z10+z8+z7+z3+z+1
L=GF(26) - GF(23)
The field GF(26) is constructed using the primitive polynomial p(x)=x6+x+1, p(α)=0;
The weight enumerator is given by: A(z)=1 + 3612 z20 + 14175 z24 + 29960 z28 + 14175 z32 + 3612 z36 + z56
From the MacWilliams transform the minimum distance of the dual code follows: C⊥ is a [56,40,6] code.
References:
M.Loeloeian, J.Conan: A [55,16,19] Binary Goppa Code, IEEE, Trans. Inf. Theory, Vol. IT-30, No.5, September 1984, pp.773.
M.Loeloeian, J.Conan: A Transform Approach to Goppa Codes, IEEE, Trans. Inf. Theory, Vol. IT-33, No.1, January 1987, pp.105-115.