the 1 isometry classes of irreducible [40,36,3]_3 codes are: code no 1: ================ 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 the automorphism group has order 12130560 and is strongly generated by the following 15 elements: ( 1 0 0 0 0 2 0 0 0 0 2 0 0 0 0 1 , 1 0 0 0 0 1 0 0 0 0 2 0 0 0 0 1 , 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 1 , 2 0 0 0 0 1 0 0 0 0 2 0 1 0 1 1 , 2 0 0 0 0 2 0 0 0 0 1 0 0 0 2 2 , 2 0 0 0 0 1 0 0 0 0 2 0 0 2 0 2 , 2 0 0 0 0 1 0 0 0 0 1 0 0 2 2 1 , 2 0 0 0 0 2 0 0 2 0 2 0 2 0 0 2 , 1 0 0 0 0 1 0 0 2 1 0 2 2 1 2 0 , 2 0 0 0 0 1 0 0 0 0 0 2 1 0 2 0 , 2 0 0 0 1 0 1 2 0 0 2 2 1 1 1 0 , 1 0 0 0 1 2 0 0 0 2 1 1 0 2 2 0 , 2 0 0 0 1 1 0 1 2 2 1 2 0 1 2 2 , 0 0 0 1 0 1 2 2 2 1 1 2 0 0 1 1 , 1 1 1 2 2 2 2 0 0 2 2 2 1 0 2 0 ) acting on the columns of the generator matrix as follows (in order): (5, 39)(6, 7)(8, 9)(11, 12)(14, 15)(18, 21)(19, 22)(20, 23)(24, 32)(25, 33)(26, 34)(27, 38)(28, 40)(29, 35)(30, 36)(31, 37), (5, 36)(8, 9)(10, 13)(11, 15)(12, 14)(24, 32)(25, 33)(26, 34)(27, 35)(28, 37)(29, 38)(30, 39)(31, 40), (5, 40)(16, 17)(18, 21)(19, 23)(20, 22)(24, 32)(25, 34)(26, 33)(27, 38)(28, 39)(29, 35)(30, 37)(31, 36), (4, 25)(5, 18)(6, 7)(10, 13)(11, 14)(12, 15)(16, 24)(17, 26)(19, 27)(20, 28)(21, 30)(22, 29)(23, 31)(32, 33)(35, 36)(38, 39), (4, 24)(5, 19)(8, 9)(10, 13)(11, 15)(12, 14)(16, 25)(17, 26)(18, 27)(20, 28)(21, 29)(22, 30)(23, 31), (4, 18)(5, 25)(6, 7)(10, 13)(11, 14)(12, 15)(16, 19)(17, 20)(24, 27)(26, 28)(32, 35)(33, 36)(34, 37), (4, 27, 38)(5, 40, 16, 28, 39, 17)(6, 7)(8, 9)(11, 12)(14, 15)(18, 29, 32)(19, 31, 33, 20, 30, 34)(21, 24, 35)(22, 26, 36, 23, 25, 37), (3, 9, 8)(4, 17, 16)(5, 28, 27)(10, 12, 11)(13, 15, 14)(18, 20, 19)(21, 23, 22)(24, 25, 26)(29, 30, 31), (3, 22)(4, 14)(5, 25)(8, 21)(9, 23)(10, 19)(11, 18)(12, 20)(13, 16)(15, 17)(24, 28)(26, 27)(29, 31), (3, 16, 8, 17, 9, 4)(5, 31, 27, 30, 28, 29)(6, 7)(10, 22, 11, 23, 12, 21)(13, 19, 14, 20, 15, 18)(24, 25, 26)(32, 33)(35, 36)(38, 39), (2, 37, 34)(3, 15, 31, 19, 23, 24)(4, 11)(6, 36, 32)(7, 35, 33)(8, 14, 30, 18, 21, 25)(9, 13, 29, 20, 22, 26)(10, 16)(12, 17)(27, 28), (2, 7)(3, 22, 31, 9, 23, 29)(4, 28, 11, 17, 5, 10)(8, 21, 30)(12, 16, 27)(13, 20, 26)(14, 19, 25, 15, 18, 24)(33, 34)(35, 37)(38, 39), (2, 30, 16, 25, 36, 3, 10, 19)(4, 26, 35, 9, 11, 20, 7, 29)(5, 13, 33, 22)(6, 31, 17, 24, 37, 8, 12, 18)(14, 32, 23, 28, 15, 34, 21, 27), (1, 31, 28, 9, 37, 25, 15, 5, 39, 3, 17, 29, 2, 18, 19, 11, 38, 23, 10, 22, 34, 14, 24, 4)(6, 12, 8, 13)(7, 33, 35)(16, 30, 26, 36, 27, 21, 20, 32), (1, 12, 9, 4, 6, 36, 37, 24, 34, 25, 29, 17, 13, 18, 30, 5, 7, 21, 27, 3, 39, 10, 15, 33, 23, 40)(2, 26, 19, 32, 35, 22, 16, 8, 28, 14, 31, 38, 11) orbits: { 1, 4, 40, 25, 24, 18, 38, 16, 14, 9, 11, 10, 29, 28, 31, 5, 23, 33, 34, 21, 19, 37, 32, 27, 26, 17, 15, 30, 12, 2, 13, 39, 3, 22, 8, 35, 7, 20, 36, 6 }