#  MAPLE.  June 5. 2006.
#
#  Take dual of coset graph of shortened ternary Golay code.
#  This is Q-antipodal. So delete one class to get a new scheme.
with(linalg):
d := 4;
v := [1 ,   36 ,  60 ,   45 ,  20];
verts := 162;


Q := matrix([
[1 ,  20 ,  120 ,  20 ,   1],
[1 ,   5 ,    0 ,  -5 ,  -1],
[1 ,   2 ,   -6 ,   2 ,   1],
[1 ,  -4 ,    0 ,   4 ,  -1],
[1 ,  -7 ,   12 ,  -7 ,   1]
]);

#  This tridiagonal  matrix, L_1-star,  allows us to fill out the cols of Q
#  if we are only given the cosines (normalized column 1 of Q).
L := matrix([
[0 ,  20 ,   0 ,   0 ,  0],
[1 ,   1 ,  18 ,   0 ,  0],
[0 ,   3 ,  14 ,   3 ,  0],
[0 ,   0 ,  18 ,   1 ,  1],
[0 ,   0 ,   0 ,  20 ,  0]
]);

        [0    36     0     0     0]
        [                         ]
        [1     0    30     0     5]
        [                         ]
L_1  =  [0    18     0    18     0]
        [                         ]
        [0     0    24     0    12]
        [                         ]
        [0     9     0    27     0]
 
        [0     0    60     0     0]
        [                         ]
        [0    30     0    30     0]
        [                         ]
L_2  =  [1     0    45     0    14]
        [                         ]
        [0    24     0    36     0]
        [                         ]
        [0     0    42     0    18]
 
        [0     0     0    45     0]
        [                         ]
        [0     0    30     0    15]
        [                         ]
L_3  =  [0    18     0    27     0]
        [                         ]
        [1     0    36     0     8]
        [                         ]
        [0    27     0    18     0]
 
        [0     0     0     0    20]
        [                         ]
        [0     5     0    15     0]
        [                         ]
L_4  =  [0     0    14     0     6]
        [                         ]
        [0    12     0     8     0]
        [                         ]
        [1     0    18     0     1]
 


       [1     36    60     45    20]
       [                           ]
       [1      9     6     -9    -7]
       [                           ]
 P  =  [1      0    -3      0     2]
       [                           ]
       [1     -9     6      9    -7]
       [                           ]
       [1    -36    60    -45    20]
 

       [1    20    120    20     1]
       [                          ]
       [1     5      0    -5    -1]
       [                          ]
 Q  =  [1     2     -6     2     1]
       [                          ]
       [1    -4      0     4    -1]
       [                          ]
       [1    -7     12    -7     1]
 


          [0    20     0     0    0]
          [                        ]
          [1     1    18     0    0]
          [                        ]
  Ls1  =  [0     3    14     3    0]
          [                        ]
          [0     0    18     1    1]
          [                        ]
          [0     0     0    20    0]
 
          [0     0    120     0    0]
          [                         ]
          [0    18     84    18    0]
          [                         ]
  Ls2  =  [1    14     90    14    1]
          [                         ]
          [0    18     84    18    0]
          [                         ]
          [0     0    120     0    0]
 
          [0     0     0    20    0]
          [                        ]
          [0     0    18     1    1]
          [                        ]
  Ls3  =  [0     3    14     3    0]
          [                        ]
          [1     1    18     0    0]
          [                        ]
          [0    20     0     0    0]
 
          [0    0    0    0    1]
          [                     ]
          [0    0    0    1    0]
          [                     ]
  Ls4  =  [0    0    1    0    0]
          [                     ]
          [0    1    0    0    0]
          [                     ]
          [1    0    0    0    0]