// An extremal doubly even self-dual code of length 112
// http://sci.kj.yamagata-u.ac.jp/~mharada/Paper/112.magma
// This is written in Magma format

A:=Matrix(GF(2),28,28,[
1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1, 
1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1, 
1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1, 
1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0, 
0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0, 
0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1, 
1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1, 
1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1, 
1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1, 
1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0, 
0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0, 
0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1, 
1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0, 
0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1, 
1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0, 
0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0, 
0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0, 
0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0, 
0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0, 
0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0, 
0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0, 
0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0, 
0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,1, 
1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0, 
0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1, 
1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0, 
0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0, 
0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1
]); 

B:=Matrix(GF(2),28,28,[
1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,
1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,
1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,
0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,
1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,
1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,
1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,
1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,
0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,
1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,
1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,
1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,
1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,
0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,
0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,
0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,
0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,
1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,
1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,
1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,
1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,
1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,
0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,
0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,
1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,
1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,
1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,
0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1
]);

AT:=Transpose(A);
BT:=Transpose(B);

gen:=HorizontalJoin(ScalarMatrix(56,GF(2)!1),
VerticalJoin(HorizontalJoin(A,B),HorizontalJoin(BT,AT)));
C:=LinearCode(gen);

"IsSelfDual=",IsSelfDual(C);
"IsDoublyEven=",IsDoublyEven(C);
"MinimumWeight=",MinimumWeight(C);
X:=AutomorphismGroup(C);
"#Aut(C)=",#X;
"IsTransitive=",IsTransitive(X);
"Dimension of subcode generated by the minimum weight=",
Dimension(LinearCode<GF(2),112|Words(C,20)>);

/*
Magma V2.14-11    Wed May 14 2008 08:56:37 on kd0scl1  [Seed = 3800072285]
Type ? for help.  Type <Ctrl>-D to quit.
IsSelfDual= true
IsDoublyEven= true
MinimumWeight= 20
#Aut(C)= 112
IsTransitive= true
Dimension of subcode generated by the minimum weight= 56

Total time: 2561.869 seconds, Total memory usage: 222.75MB
*/