 LIB "brnoeth.lib";
int plevel=printlevel;
printlevel=1;
ring s=2,(x,y),lp;
list HC=Adj_div(x3+y2+y);
==> The genus of the curve is 1
HC=NSplaces(1..2,HC);
HC=extcurve(2,HC);
==> Total number of rational places : NrRatPl = 9
def ER=HC[1][4];
setring ER;
intvec G=5; // the rational divisor G = 5*HC[3][1]
intvec D=2..9; // D = sum of the rational places no. 2..9 over F_4
// construct the corresp. residual AG code of type [8,3,>=5] over F_4:
matrix C=AGcode_Omega(G,D,HC);
==> Vector basis successfully computed
// we can correct 1 error and the genus is 1, thus F must have degree 2
// and support disjoint from that of D;
intvec F=2;
list SV=prepSV(G,D,F,HC);
==> Vector basis successfully computed
==> Vector basis successfully computed
==> Vector basis successfully computed
// now everything is prepared to decode with the basic algorithm;
// for example, here is a parity check matrix to compute the syndrome :
print(SV[1]);
==> 0,0,1, 1, (a+1),(a), (a), (a+1),
==> 0,1,(a),(a+1),(a), (a+1),(a), (a+1),
==> 1,1,1, 1, 1, 1, 1, 1,
==> 0,0,1, 1, (a), (a+1),(a+1),(a),
==> 0,0,(a),(a+1),1, 1, (a+1),(a)
// and here you have the correction capacity of the algorithm :
int epsilon=SV[size(D)+3][1];
epsilon;
==> 1
printlevel=plevel;
