#  MAPLE.  June 5. 2006.
#
#  Take dual of coset graph of the shortened extended ternary Golay code.
#  This is Q-antipodal with r=3. So delete one class to get a new scheme.
with(linalg):
d := 5;
v := [1 ,   66 ,  132 ,   165 ,  110 ,   12];
verts := 486;


Q := matrix([
[1 ,   22 ,  220 ,  220 ,  22 ,   1],
[1 ,    7 ,   10 ,  -10 ,  -7 ,  -1],
[1 ,    4 ,   -5 ,   -5 ,   4 ,   1],
[1 ,   -2 ,   -8 ,    8 ,   2 ,  -1],
[1 ,   -5 ,    4 ,    4 ,  -5 ,   1],
[1 ,  -11 ,   55 ,  -55 ,  11 ,  -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 ,  22 ,   0   ,   0   ,   0 ,  0],
[1 ,   1 ,   20  ,   0   ,   0 ,  0],
[0 ,   2 ,  13/2 ,  27/2 ,   0 ,  0],
[0 ,   0 ,  27/2 ,  13/2 ,   2 ,  0],
[0 ,   0 ,   0   ,   20  ,   1 ,  1],
[0 ,   0 ,   0   ,   0   ,  22 ,  0]
]);


       [0    66     0     0     0    0]
       [                              ]
       [1     0    50     0    15    0]
       [                              ]
       [0    25     0    40     0    1]
L_1  = [                              ]
       [0     0    32     0    34    0]
       [                              ]
       [0     9     0    51     0    6]
       [                              ]
       [0     0    11     0    55    0]

     [0     0    132      0     0     0]
     [                                 ]
     [0    50      0     80     0     2]
     [                                 ]
     [1     0     81      0    50     0]
L_2 =[                                 ]
     [0    32      0     92     0     8]
     [                                 ]
     [0     0     60      0    72     0]
     [                                 ]
     [0    11      0    110     0    11]

     [0     0      0    165     0     0]
     [                                 ]
     [0     0     80      0    85     0]
     [                                 ]
     [0    40      0    115     0    10]
L_3 =[                                 ]
     [1     0     92      0    72     0]
     [                                 ]
     [0    51      0    108     0     6]
     [                                 ]
     [0     0    110      0    55     0]

      [0     0     0     0    110     0]
      [                                ]
      [0    15     0    85      0    10]
      [                                ]
      [0     0    50     0     60     0]
L_4 = [                                ]
      [0    34     0    72      0     4]
      [                                ]
      [1     0    72     0     37     0]
      [                                ]
      [0    55     0    55      0     0]

       [0    0     0     0     0    12]
       [                              ]
       [0    0     2     0    10     0]
       [                              ]
       [0    1     0    10     0     1]
L_5 =  [                              ]
       [0    0     8     0     4     0]
       [                              ]
       [0    6     0     6     0     0]
       [                              ]
       [1    0    11     0     0     0]



        [1     66    132     165    110     12]
        [                                     ]
        [1     21     24     -15    -25     -6]
        [                                     ]
        [1      3     -3      -6      2      3]
  P  =  [                                     ]
        [1     -3     -3       6      2     -3]
        [                                     ]
        [1    -21     24      15    -25      6]
        [                                     ]
        [1    -66    132    -165    110    -12]


        [1     22    220    220    22     1]
        [                                  ]
        [1      7     10    -10    -7    -1]
        [                                  ]
        [1      4     -5     -5     4     1]
  Q  =  [                                  ]
        [1     -2     -8      8     2    -1]
        [                                  ]
        [1     -5      4      4    -5     1]
        [                                  ]
        [1    -11     55    -55    11    -1]





     [0    22     0       0       0    0]
     [                                  ]
     [1     1     20      0       0    0]
     [                                  ]
     [0     2    13/2    27/2     0    0]
Ls1 =[                                  ]
     [0     0    27/2    13/2     2    0]
     [                                  ]
     [0     0     0       20      1    1]
     [                                  ]
     [0     0     0       0      22    0]

    [0     0      220      0     0      0]
    [                                    ]
    [0     20      65    135     0      0]
    [                                    ]
    [1    13/2    118     81    27/2    0]
Ls2=[                                    ]
    [0    27/2     81    118    13/2    1]
    [                                    ]
    [0     0      135     65     20     0]
    [                                    ]
    [0     0        0    220     0      0]

    [0     0        0    220     0      0]
    [                                    ]
    [0     0      135     65     20     0]
    [                                    ]
    [0    27/2     81    118    13/2    1]
Ls3=[                                    ]
    [1    13/2    118     81    27/2    0]
    [                                    ]
    [0     20      65    135     0      0]
    [                                    ]
    [0     0      220      0     0      0]

     [0     0     0       0      22    0]
     [                                  ]
     [0     0     0       20      1    1]
     [                                  ]
     [0     0    27/2    13/2     2    0]
Ls4 =[                                  ]
     [0     2    13/2    27/2     0    0]
     [                                  ]
     [1     1     20      0       0    0]
     [                                  ]
     [0    22     0       0       0    0]

         [0    0    0    0    0    1]
         [                          ]
         [0    0    0    0    1    0]
         [                          ]
         [0    0    0    1    0    0]
  Ls5  = [                          ]
         [0    0    1    0    0    0]
         [                          ]
         [0    1    0    0    0    0]
         [                          ]
         [1    0    0    0    0    0]