the 19 isometry classes of irreducible [10,4,5]_3 codes are: code no 1: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 1 2 1 0 1 0 0 0 2 0 2 2 0 1 1 0 0 0 0 2 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 1 1 1 1 1 1 , 0 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 1 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (6, 7), (1, 2)(4, 5)(6, 7)(8, 9) orbits: { 1, 2 }, { 3 }, { 4, 5 }, { 6, 7 }, { 8, 9 }, { 10 } code no 2: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 1 2 1 0 1 0 0 0 2 0 2 2 1 0 0 1 0 0 0 2 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (1, 2)(4, 5)(8, 9) orbits: { 1, 2 }, { 3 }, { 4, 5 }, { 6 }, { 7 }, { 8, 9 }, { 10 } code no 3: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 1 2 1 0 1 0 0 0 2 0 1 0 2 1 0 1 0 0 0 2 the automorphism group has order 10 and is strongly generated by the following 3 elements: ( 1 0 0 0 0 0 1 2 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 2 , 0 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 1 1 1 1 1 1 , 2 0 1 2 0 2 2 1 1 1 0 0 0 0 0 0 0 2 0 0 0 1 0 0 2 2 2 2 2 2 0 0 2 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (2, 9)(3, 5)(4, 7)(8, 10), (1, 2)(4, 5)(6, 7)(8, 9), (1, 10)(2, 8)(3, 6)(5, 7) orbits: { 1, 2, 10, 9, 8 }, { 3, 5, 6, 4, 7 } code no 4: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 1 2 1 0 1 0 0 0 2 0 0 1 2 1 0 1 0 0 0 2 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 2 1 2 0 2 0 1 2 2 2 0 0 1 1 1 1 1 1 , 0 1 0 0 0 0 1 0 0 0 0 0 0 0 2 0 0 0 2 1 1 1 0 0 1 2 1 0 1 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 9)(5, 8)(6, 7), (1, 2)(4, 8)(5, 9) orbits: { 1, 2 }, { 3 }, { 4, 9, 8, 5 }, { 6, 7 }, { 10 } code no 5: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 1 2 1 0 1 0 0 0 2 0 2 2 0 2 0 1 0 0 0 2 the automorphism group has order 3 and is strongly generated by the following 1 elements: ( 1 0 0 0 0 0 1 1 0 1 0 2 0 0 0 2 0 0 0 0 0 0 0 1 1 2 1 0 1 0 0 0 2 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (2, 8, 10)(3, 6, 4)(5, 7, 9) orbits: { 1 }, { 2, 10, 8 }, { 3, 4, 6 }, { 5, 9, 7 } code no 6: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 1 2 1 0 1 0 0 0 2 0 1 0 1 2 0 1 0 0 0 2 the automorphism group has order 32 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 1 2 1 0 1 0 1 0 1 2 0 1 , 2 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 1 0 1 2 0 1 1 2 1 0 1 0 , 1 2 2 2 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 0 0 0 2 0 0 1 2 2 2 0 0 0 0 1 0 0 0 2 0 0 0 0 0 1 2 1 0 1 0 0 0 0 0 0 1 , 2 0 2 1 0 2 0 0 0 0 1 0 1 1 1 1 1 1 1 2 1 0 1 0 0 2 0 0 0 0 2 1 1 1 0 0 ) acting on the columns of the generator matrix as follows (in order): (5, 9)(6, 10), (2, 4)(5, 10)(6, 9), (1, 8)(2, 4), (1, 4)(2, 8)(5, 9), (1, 10)(2, 5)(3, 7)(4, 9)(6, 8) orbits: { 1, 8, 4, 10, 2, 6, 9, 5 }, { 3, 7 } code no 7: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 1 2 1 0 1 0 0 0 2 0 1 0 0 2 2 1 0 0 0 2 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 1 2 1 0 1 0 0 0 0 0 1 0 0 0 2 0 0 0 1 2 2 2 0 0 0 1 0 0 0 0 1 1 1 1 1 1 , 0 2 0 0 0 0 2 0 0 0 0 0 0 0 1 0 0 0 1 2 2 2 0 0 2 1 2 0 2 0 1 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (1, 9)(2, 5)(4, 8)(6, 7), (1, 2)(4, 8)(5, 9)(6, 7) orbits: { 1, 9, 2, 5 }, { 3 }, { 4, 8 }, { 6, 7 }, { 10 } code no 8: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 2 2 1 0 1 0 0 0 2 0 0 1 2 1 1 0 0 0 0 2 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 1 1 1 1 1 1 , 1 0 0 0 0 0 1 1 2 0 2 0 0 2 1 2 2 0 0 0 0 1 0 0 2 1 1 1 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (6, 7), (2, 9)(3, 10)(5, 8) orbits: { 1 }, { 2, 9 }, { 3, 10 }, { 4 }, { 5, 8 }, { 6, 7 } code no 9: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 2 2 1 0 1 0 0 0 2 0 2 1 2 0 0 1 0 0 0 2 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (2, 3)(5, 6)(9, 10) orbits: { 1 }, { 2, 3 }, { 4 }, { 5, 6 }, { 7 }, { 8 }, { 9, 10 } code no 10: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 2 2 1 0 1 0 0 0 2 0 2 2 2 0 0 1 0 0 0 2 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 0 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 2 2 2 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (1, 3)(4, 5)(6, 10)(8, 9) orbits: { 1, 3 }, { 2 }, { 4, 5 }, { 6, 10 }, { 7 }, { 8, 9 } code no 11: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 2 2 1 0 1 0 0 0 2 0 0 2 1 1 0 1 0 0 0 2 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 2 1 1 1 0 0 0 0 0 2 0 0 0 1 2 2 0 2 1 1 2 0 2 0 , 0 1 0 0 0 0 1 0 0 0 0 0 0 2 1 1 0 1 2 2 2 2 2 2 1 2 2 2 0 0 2 2 1 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (3, 8)(5, 10)(6, 9), (1, 2)(3, 10)(4, 7)(5, 8)(6, 9) orbits: { 1, 2 }, { 3, 8, 10, 5 }, { 4, 7 }, { 6, 9 } code no 12: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 2 2 1 0 1 0 0 0 2 0 0 1 1 2 0 1 0 0 0 2 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 } code no 13: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 2 2 1 0 1 0 0 0 2 0 2 1 0 0 2 1 0 0 0 2 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 1 1 1 1 1 1 0 2 0 0 0 0 0 0 2 0 0 0 , 2 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 2 0 1 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (2, 5)(3, 6)(4, 7)(9, 10), (1, 8)(3, 4)(6, 7) orbits: { 1, 8 }, { 2, 5 }, { 3, 6, 4, 7 }, { 9, 10 } code no 14: ================ 1 1 1 1 1 1 2 0 0 0 2 1 1 1 0 0 0 2 0 0 2 2 1 0 1 0 0 0 2 0 1 0 0 2 2 1 0 0 0 2 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 0 0 0 0 2 0 0 1 0 0 0 0 1 1 2 0 2 0 2 1 1 1 0 0 2 0 0 0 0 0 0 0 0 0 0 2 , 2 1 1 1 0 0 0 0 0 0 0 2 1 1 1 1 1 1 0 0 0 0 2 0 0 0 0 1 0 0 0 1 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(3, 9)(4, 8)(7, 10), (1, 8)(2, 6)(3, 7)(4, 5)(9, 10) orbits: { 1, 5, 8, 4 }, { 2, 6 }, { 3, 9, 7, 10 } code no 15: ================ 1 1 1 1 1 1 2 0 0 0 2 2 1 1 0 0 0 2 0 0 2 1 2 0 1 0 0 0 2 0 0 2 2 1 1 0 0 0 0 2 the automorphism group has order 32 and is strongly generated by the following 3 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 1 1 1 1 1 1 , 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 2 , 2 2 1 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 1 2 1 0 2 0 0 0 2 0 0 0 2 2 2 2 2 2 ) acting on the columns of the generator matrix as follows (in order): (6, 7), (2, 3)(4, 5)(8, 9), (1, 3, 5, 2, 10, 9, 4, 8)(6, 7) orbits: { 1, 8, 9, 4, 10, 5, 2, 3 }, { 6, 7 } code no 16: ================ 1 1 1 1 1 1 2 0 0 0 2 2 1 1 0 0 0 2 0 0 2 1 2 0 1 0 0 0 2 0 1 2 2 0 0 1 0 0 0 2 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 2 2 0 0 1 2 1 0 2 0 2 1 1 0 0 2 , 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 2 , 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 2 1 1 0 0 2 1 1 2 2 0 0 1 2 1 0 2 0 ) acting on the columns of the generator matrix as follows (in order): (4, 8)(5, 9)(6, 10), (2, 3)(4, 5)(8, 9), (1, 3, 2)(4, 9, 6, 8, 5, 10) orbits: { 1, 2, 3 }, { 4, 8, 5, 10, 9, 6 }, { 7 } code no 17: ================ 1 1 1 1 1 1 2 0 0 0 2 2 1 1 0 0 0 2 0 0 2 1 2 0 1 0 0 0 2 0 2 1 0 2 0 1 0 0 0 2 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 , 2 0 0 0 0 0 0 0 0 1 0 0 2 2 1 1 0 0 0 1 0 0 0 0 1 2 1 0 2 0 0 0 0 0 0 2 , 1 0 0 0 0 0 0 0 2 0 0 0 1 1 2 2 0 0 0 2 0 0 0 0 2 1 0 2 0 1 0 0 0 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(5, 6)(9, 10), (2, 4)(3, 8)(5, 9), (2, 4, 8, 3)(5, 6, 9, 10) orbits: { 1 }, { 2, 4, 3, 8 }, { 5, 6, 9, 10 }, { 7 } code no 18: ================ 1 1 1 1 0 0 2 0 0 0 2 1 1 0 1 0 0 2 0 0 1 2 0 1 1 0 0 0 2 0 1 2 1 0 0 1 0 0 0 2 the automorphism group has order 16 and is strongly generated by the following 3 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 1 2 1 0 0 1 , 2 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 2 2 0 2 0 2 2 2 2 0 0 0 0 0 0 0 2 , 2 2 2 2 0 0 0 0 0 2 0 0 0 2 0 0 0 0 2 1 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (6, 10), (2, 3)(4, 8)(5, 7), (1, 5, 9, 7)(2, 3, 8, 4) orbits: { 1, 7, 5, 9 }, { 2, 3, 4, 8 }, { 6, 10 } code no 19: ================ 1 1 1 1 0 0 2 0 0 0 2 1 1 0 1 0 0 2 0 0 2 1 0 1 0 1 0 0 2 0 1 1 0 0 1 1 0 0 0 2 the automorphism group has order 72 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 2 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 , 2 0 0 0 0 0 0 0 2 0 0 0 1 1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 1 2 1 1 0 1 0 , 1 0 0 0 0 0 1 1 0 0 1 1 1 2 0 2 0 2 0 0 0 0 2 0 1 2 2 0 2 0 0 0 0 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (4, 5)(7, 8)(9, 10), (3, 4)(5, 6)(8, 9), (3, 5)(4, 6)(7, 10), (2, 4, 7, 3)(5, 9, 8, 6), (2, 9, 3, 10)(4, 7, 8, 5) orbits: { 1 }, { 2, 3, 10, 4, 5, 7, 9, 6, 8 }