#  MAPLE.   June 4, 2006.
#
#  Supports of weight 6 vectors in extended ternary Golay code.
#  These form a 5-(12,6,1) design.
d := 4;
v := [1 ,  45 ,  40 ,   45 ,   1];
verts := 132;

Q := matrix([
[1 ,   11   ,   54   ,   55   ,   11  ],
[1 ,  11/3  ,   6/5  ,  -11/3 ,  -11/5],
[1 ,    0   ,  -27/5 ,    0   ,  22/5 ],
[1 ,  -11/3 ,   6/5  ,  11/3  ,  -11/5],
[1 ,   -11  ,   54   ,   -55  ,   11  ]
]);


# Tridiagonal matrix L = L1-star can be used to obtain Q (and
# then all parameters) from just the cosines.
L := matrix([
[0 ,  11  ,  0  ,    0   ,  0  ],
[1 ,  0   ,  10 ,    0   ,  0  ],
[0 , 55/27,  0  , 242/27 ,  0  ],
[0 ,  0   , 44/5,    0   , 11/5],
[0 ,  0   ,  0  ,   11   ,  0  ]
]);

       [0    45     0     0    0]
       [                        ]
       [1    20    16     8    0]
       [                        ]
L_1  = [0    18     9    18    0]
       [                        ]
       [0     8    16    20    1]
       [                        ]
       [0     0     0    45    0]

       [0     0    40     0    0]
       [                        ]
       [0    16     8    16    0]
       [                        ]
L_2  = [1     9    20     9    1]
       [                        ]
       [0    16     8    16    0]
       [                        ]
       [0     0    40     0    0]

       [0     0     0    45    0]
       [                        ]
       [0     8    16    20    1]
       [                        ]
L_3  = [0    18     9    18    0]
       [                        ]
       [1    20    16     8    0]
       [                        ]
       [0    45     0     0    0]

        [0    0    0    0    1]
        [                     ]
        [0    0    0    1    0]
        [                     ]
L_4  =  [0    0    1    0    0]
        [                     ]
        [0    1    0    0    0]
        [                     ]
        [1    0    0    0    0]


         [1    45    40     45     1]
         [                          ]
         [1    15     0    -15    -1]
         [                          ]
  P  =   [1     1    -4      1     1]
         [                          ]
         [1    -3     0      3    -1]
         [                          ]
         [1    -9    16     -9     1]

  [1     11       54       55       11  ]
  [                                     ]
  [1    11/3      6/5     -11/3    -11/5]
  [                                     ]
Q=[1      0      -27/5      0      22/5 ]
  [                                     ]
  [1    -11/3     6/5     11/3     -11/5]
  [                                     ]
  [1     -11      54       -55      11  ]


         [0    11     0       0      0  ]
         [                              ]
         [1    0      10      0      0  ]
         [                              ]
         [     55            242        ]
Ls1  =   [0    --     0      ---     0  ]
         [     27            27         ]
         [                              ]
         [0    0     44/5     0     11/5]
         [                              ]
         [0    0      0      11      0  ]

       [0     0       54       0       0 ]
       [                                 ]
       [0     10      0       44       0 ]
       [                                 ]
       [             1083             242]
       [1     0      ----      0      ---]
Ls2  = [              25              25 ]
       [                                 ]
       [0    44/5     0      226/5     0 ]
       [                                 ]
       [             1188             162]
       [0     0      ----      0      ---]
       [              25              25 ]

       [0     0       0       55      0  ]
       [                                 ]
       [0     0      44       0       11 ]
       [                                 ]
       [     242             1243        ]
Ls3  = [0    ---      0      ----     0  ]
       [     27               27         ]
       [                                 ]
       [1     0     226/5     0      44/5]
       [                                 ]
       [0    11       0       44      0  ]

         [0     0       0      0      11]
         [                              ]
         [0     0       0      11     0 ]
         [                              ]
         [             242            33]
         [0     0      ---     0      --]
Ls4  =   [             25             25]
         [                              ]
         [0    11/5     0     44/5    0 ]
         [                              ]
         [             162            88]
         [1     0      ---     0      --]
         [             25             25]