# MAPLE.  June 4, 2006.
#
# 4-class Q-bipartite cometric association scheme
# defined on blocks of the 5-(24,12,48) design from the Golay code.
d := 4;
v := [1, 495, 1584, 495, 1];
verts := 2576;


Q := matrix([
[1 ,   23  ,   252  ,  1265 ,   1035],
[1 ,  23/3 ,196/11  ,  -23/3,-207/11],
[1 ,    0  ,-126/11 ,    0  , 115/11],
[1 ,  -23/3, 196/11 ,  23/3 ,-207/11],
[1 ,   -23 ,   252  ,  -1265,   1035]
]);


# Tridiagonal matrix L = L1-star can be used to obtain Q (and
# then all parameters) from just the cosines.
L := matrix([
[0 ,  23  ,  0   ,  0  ,    0 ],
[1 ,   0  ,  22  ,  0  ,    0 ],
[0 ,253/126, 0,2645/126,    0 ],
[0 ,   0  ,46/11 ,  0  ,207/11],
[0 ,   0  ,  0   ,  23 ,    0 ]
]):



      [0    495      0      0    0]
      [                           ]
      [1    184    288     22    0]
      [                           ]
L_1 = [0     90    315     90    0]
      [                           ]
      [0     22    288    184    1]
      [                           ]
      [0      0      0    495    0]

      [0      0    1584      0    0]
      [                            ]
      [0    288    1008    288    0]
      [                            ]
L_2 = [1    315     952    315    1]
      [                            ]
      [0    288    1008    288    0]
      [                            ]
      [0      0    1584      0    0]

      [0      0      0    495    0]
      [                           ]
      [0     22    288    184    1]
      [                           ]
L_3 = [0     90    315     90    0]
      [                           ]
      [1    184    288     22    0]
      [                           ]
      [0    495      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    495    1584     495     1]
   [                              ]
   [1    165       0    -165    -1]
   [                              ]
P= [1     35     -72      35     1]
   [                              ]
   [1     -3       0       3    -1]
   [                              ]
   [1     -9      16      -9     1]

     [1     23      252     1265     1035]
     [                                   ]
     [              196              -207]
     [1    23/3     ---     -23/3    ----]
     [              11                11 ]
     [                                   ]
     [              -126             115 ]
 Q = [1      0      ----      0      --- ]
     [               11              11  ]
     [                                   ]
     [              196              -207]
     [1    -23/3    ---     23/3     ----]
     [              11                11 ]
     [                                   ]
     [1     -23     252     -1265    1035]

     [0    23     0      0       0 ]
     [                             ]
     [1     0     22     0       0 ]
     [                             ]
     [     253          2645       ]
     [0    ---    0     ----     0 ]
Ls1= [     126          126        ]
     [                             ]
     [            46            207]
     [0     0     --     0      ---]
     [            11            11 ]
     [                             ]
     [0     0     0      23      0 ]

    [0    0     252      0        0  ]
    [                                ]
    [0    22     0      230       0  ]
    [                                ]
    [           6566            23805]
    [1    0     ----     0      -----]
    [           121              121 ]
Ls2=[                                ]
    [     46            2726         ]
    [0    --     0      ----      0  ]
    [     11             11          ]
    [                                ]
    [           5796            24696]
    [0    0     ----     0      -----]
    [           121              121 ]

     [0     0       0       1265       0  ]
     [                                    ]
     [0     0      230       0       1035 ]
     [                                    ]
     [     2645            156745         ]
     [0    ----     0      ------      0  ]
Ls3 =[     126              126           ]
     [                                    ]
     [             2726              11178]
     [1     0      ----      0       -----]
     [              11                11  ]
     [                                    ]
     [0     23      0       1242       0  ]

      [0     0       0        0       1035 ]
      [                                    ]
      [0     0       0      1035       0   ]
      [                                    ]
      [            23805             101430]
      [0     0     -----      0      ------]
      [             121               121  ]
Ls4 = [                                    ]
      [     207             11178          ]
      [0    ---      0      -----      0   ]
      [     11               11            ]
      [                                    ]
      [            24696             100418]
      [1     0     -----      0      ------]
      [             121               121  ]