// Linear code over GF(5) of type [65,13,36]
// Iwan Duursma, 041604.
 
// Magma unital construction follows: load "H99E11"
// In general the construction gives codes of rate 1/(q+1)
// proof: length=q^3+1, rank is 2g+1=q^2-q+1, for 2g=q(q-1).
 
q := 4;
F<w> := GaloisField(q ^ 2);
P, V, L := FiniteProjectivePlane(F);

hu :={ V | [x,y,z] : x, y, z in F |                                     
            x^(q+1) + y^(q+1) + z^(q+1) eq 0 and {x, y, z} ne {0} };
blks := [blk : lin in L | #blk eq (q+1) where blk is lin meet hu ];

bc:=LinearCode< GF(5), #hu | 
        [ [ #(blk meet {pnt}) : pnt in hu ] : blk in blks ] >;

dbc:=Dual(bc);

[ Length(dbc), Dimension(dbc), MinimumDistance(dbc) ];