the 42 isometry classes of irreducible [8,5,3]_5 codes are: code no 1: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 3 1 0 0 0 0 4 0 4 1 0 0 0 0 0 4 the automorphism group has order 40 and is strongly generated by the following 3 elements: ( 2 0 0 0 2 0 3 3 3 , 4 0 0 3 2 0 0 0 2 , 4 3 0 3 4 0 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (3, 4), (2, 7, 6, 8), (1, 6, 2, 7) orbits: { 1, 7, 2, 8, 6 }, { 3, 4 }, { 5 } code no 2: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 3 1 0 0 0 0 4 0 1 0 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 3 0 3 0 0 2 2 2 ) acting on the columns of the generator matrix as follows (in order): (1, 2)(3, 4)(6, 7) orbits: { 1, 2 }, { 3, 4 }, { 5 }, { 6, 7 }, { 8 } code no 3: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 3 1 0 0 0 0 4 0 2 0 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 2 2 0 1 3 0 0 0 4 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(2, 6)(4, 8) orbits: { 1, 5 }, { 2, 6 }, { 3 }, { 4, 8 }, { 7 } code no 4: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 3 1 0 0 0 0 4 0 2 2 1 0 0 0 0 4 the automorphism group has order 8 and is strongly generated by the following 2 elements: ( 4 0 0 0 4 0 2 2 1 , 4 3 0 3 4 0 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (3, 8), (1, 6, 2, 7) orbits: { 1, 7, 2, 6 }, { 3, 8 }, { 4 }, { 5 } code no 5: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 1 0 1 0 0 0 4 0 2 0 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 0 0 0 0 4 0 4 0 ) acting on the columns of the generator matrix as follows (in order): (2, 3)(5, 7)(6, 8) orbits: { 1 }, { 2, 3 }, { 4 }, { 5, 7 }, { 6, 8 } code no 6: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 1 0 1 0 0 0 4 0 3 0 1 0 0 0 0 4 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 } code no 7: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 1 0 1 0 0 0 4 0 4 0 1 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 3 0 0 2 0 3 3 3 0 , 2 0 0 3 0 3 3 3 0 ) acting on the columns of the generator matrix as follows (in order): (2, 8)(3, 5)(6, 7), (2, 7)(3, 5)(6, 8) orbits: { 1 }, { 2, 8, 7, 6 }, { 3, 5 }, { 4 } code no 8: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 1 0 1 0 0 0 4 0 0 1 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 0 0 0 3 0 2 2 2 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(7, 8) orbits: { 1 }, { 2 }, { 3, 4 }, { 5 }, { 6 }, { 7, 8 } code no 9: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 1 0 1 0 0 0 4 0 2 1 1 0 0 0 0 4 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 2 0 0 0 2 0 1 3 3 , 3 0 0 4 2 0 2 0 2 , 1 1 0 0 4 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (3, 8)(4, 7), (2, 6)(3, 7)(4, 8), (1, 5)(4, 7) orbits: { 1, 5 }, { 2, 6 }, { 3, 8, 7, 4 } code no 10: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 1 0 1 0 0 0 4 0 3 1 1 0 0 0 0 4 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 } code no 11: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 1 0 1 0 0 0 4 0 4 1 1 0 0 0 0 4 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 } code no 12: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 1 0 1 0 0 0 4 0 4 2 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 1 1 0 0 4 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(4, 7) orbits: { 1, 5 }, { 2 }, { 3 }, { 4, 7 }, { 6 }, { 8 } code no 13: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 1 0 1 0 0 0 4 0 2 3 1 0 0 0 0 4 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 } code no 14: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 1 0 1 0 0 0 4 0 3 4 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 1 1 0 0 4 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(4, 7) orbits: { 1, 5 }, { 2 }, { 3 }, { 4, 7 }, { 6 }, { 8 } code no 15: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 2 0 1 0 0 0 4 0 3 0 1 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 1 0 0 3 4 0 0 0 4 , 1 0 0 4 0 3 3 3 0 ) acting on the columns of the generator matrix as follows (in order): (2, 6)(7, 8), (2, 7, 6, 8)(3, 5) orbits: { 1 }, { 2, 6, 8, 7 }, { 3, 5 }, { 4 } code no 16: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 2 0 1 0 0 0 4 0 3 1 1 0 0 0 0 4 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 4 0 0 0 4 0 3 1 1 , 1 0 0 3 4 0 3 0 4 , 2 2 0 1 3 0 0 0 4 ) acting on the columns of the generator matrix as follows (in order): (3, 8)(4, 7), (2, 6)(3, 7)(4, 8), (1, 5)(2, 6)(4, 7) orbits: { 1, 5 }, { 2, 6 }, { 3, 8, 7, 4 } code no 17: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 2 0 1 0 0 0 4 0 4 1 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 0 0 0 3 0 2 2 2 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(7, 8) orbits: { 1 }, { 2 }, { 3, 4 }, { 5 }, { 6 }, { 7, 8 } code no 18: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 2 0 1 0 0 0 4 0 0 2 1 0 0 0 0 4 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 } code no 19: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 2 0 1 0 0 0 4 0 1 2 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 2 2 0 1 3 0 0 0 4 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(2, 6)(4, 7) orbits: { 1, 5 }, { 2, 6 }, { 3 }, { 4, 7 }, { 8 } code no 20: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 2 0 1 0 0 0 4 0 3 2 1 0 0 0 0 4 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 } code no 21: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 2 0 1 0 0 0 4 0 4 3 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 2 2 0 1 3 0 0 0 4 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(2, 6)(4, 7) orbits: { 1, 5 }, { 2, 6 }, { 3 }, { 4, 7 }, { 8 } code no 22: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 0 2 1 0 0 0 4 0 1 2 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 3 0 0 2 0 0 1 3 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(3, 7)(4, 8) orbits: { 1, 5 }, { 2 }, { 3, 7 }, { 4, 8 }, { 6 } code no 23: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 0 2 1 0 0 0 4 0 3 2 1 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 3 3 0 4 2 0 3 2 1 , 2 1 0 3 0 0 0 4 2 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(2, 6)(3, 8)(4, 7), (1, 2, 5, 6)(3, 4, 8, 7) orbits: { 1, 5, 6, 2 }, { 3, 8, 7, 4 } code no 24: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 0 2 1 0 0 0 4 0 3 3 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 3 1 0 0 4 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (1, 8)(2, 3)(4, 6) orbits: { 1, 8 }, { 2, 3 }, { 4, 6 }, { 5 }, { 7 } code no 25: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 0 2 1 0 0 0 4 0 4 3 1 0 0 0 0 4 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 } code no 26: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 0 2 1 0 0 0 4 0 1 4 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 0 0 0 3 0 2 2 2 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(7, 8) orbits: { 1 }, { 2 }, { 3, 4 }, { 5 }, { 6 }, { 7, 8 } code no 27: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 1 0 0 0 4 0 0 2 3 1 0 0 0 4 0 4 3 1 0 0 0 0 4 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 4 0 0 0 4 0 1 1 1 , 2 0 0 1 3 0 2 2 2 , 4 4 0 0 1 0 2 4 3 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(7, 8), (2, 6)(3, 4), (1, 5)(3, 7, 4, 8) orbits: { 1, 5 }, { 2, 6 }, { 3, 4, 8, 7 } code no 28: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 1 0 1 0 0 4 0 0 0 1 1 0 0 0 4 0 3 2 1 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 4 4 4 0 0 1 0 1 0 , 0 0 2 2 0 0 3 3 3 ) acting on the columns of the generator matrix as follows (in order): (1, 4)(2, 3), (1, 2, 4, 3)(5, 6) orbits: { 1, 4, 3, 2 }, { 5, 6 }, { 7 }, { 8 } code no 29: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 1 0 1 0 0 4 0 0 3 1 1 0 0 0 4 0 0 2 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 0 1 4 4 4 1 0 0 ) acting on the columns of the generator matrix as follows (in order): (1, 3)(2, 4)(7, 8) orbits: { 1, 3 }, { 2, 4 }, { 5 }, { 6 }, { 7, 8 } code no 30: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 1 0 1 0 0 4 0 0 3 1 1 0 0 0 4 0 4 2 1 0 0 0 0 4 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 } code no 31: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 1 0 1 0 0 4 0 0 4 2 1 0 0 0 4 0 2 3 1 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 1 0 0 4 4 0 4 0 4 , 1 0 0 0 0 1 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (2, 5)(3, 6), (2, 3)(5, 6)(7, 8) orbits: { 1 }, { 2, 5, 3, 6 }, { 4 }, { 7, 8 } code no 32: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 0 1 0 0 4 0 0 2 1 1 0 0 0 4 0 0 2 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 0 0 3 3 3 4 0 2 ) acting on the columns of the generator matrix as follows (in order): (2, 4)(3, 6)(5, 7) orbits: { 1 }, { 2, 4 }, { 3, 6 }, { 5, 7 }, { 8 } code no 33: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 0 1 0 0 4 0 0 2 1 1 0 0 0 4 0 1 2 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 0 0 3 3 3 4 0 2 ) acting on the columns of the generator matrix as follows (in order): (2, 4)(3, 6)(5, 7) orbits: { 1 }, { 2, 4 }, { 3, 6 }, { 5, 7 }, { 8 } code no 34: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 0 1 0 0 4 0 0 4 1 1 0 0 0 4 0 1 2 1 0 0 0 0 4 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 } code no 35: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 0 1 0 0 4 0 0 4 1 1 0 0 0 4 0 3 2 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 0 3 4 1 3 2 0 0 ) acting on the columns of the generator matrix as follows (in order): (1, 3)(2, 8)(5, 7) orbits: { 1, 3 }, { 2, 8 }, { 4 }, { 5, 7 }, { 6 } code no 36: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 0 1 0 0 4 0 0 4 1 1 0 0 0 4 0 2 3 1 0 0 0 0 4 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 } code no 37: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 0 1 0 0 4 0 0 1 2 1 0 0 0 4 0 3 2 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 2 0 0 3 3 0 2 4 2 ) acting on the columns of the generator matrix as follows (in order): (2, 5)(3, 7)(6, 8) orbits: { 1 }, { 2, 5 }, { 3, 7 }, { 4 }, { 6, 8 } code no 38: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 0 1 0 0 4 0 0 1 2 1 0 0 0 4 0 2 4 1 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 1 0 0 0 0 3 0 2 0 , 2 4 2 0 0 4 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (2, 3)(4, 8)(5, 6), (1, 7)(2, 3)(4, 6)(5, 8) orbits: { 1, 7 }, { 2, 3 }, { 4, 8, 6, 5 } code no 39: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 2 0 1 0 0 4 0 0 3 2 1 0 0 0 4 0 1 3 1 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 1 1 1 0 0 4 0 4 0 ) acting on the columns of the generator matrix as follows (in order): (1, 4)(2, 3)(6, 8) orbits: { 1, 4 }, { 2, 3 }, { 5 }, { 6, 8 }, { 7 } code no 40: ================ 1 1 1 4 0 0 0 0 1 1 0 0 4 0 0 0 3 2 1 0 0 4 0 0 4 2 1 0 0 0 4 0 2 4 1 0 0 0 0 4 the automorphism group has order 8 and is strongly generated by the following 2 elements: ( 1 0 0 1 3 4 4 3 2 , 1 1 0 0 4 0 1 3 4 ) acting on the columns of the generator matrix as follows (in order): (2, 7)(3, 8)(5, 6), (1, 5)(3, 7)(4, 6) orbits: { 1, 5, 6, 4 }, { 2, 7, 3, 8 } code no 41: ================ 1 1 1 4 0 0 0 0 2 1 0 0 4 0 0 0 3 1 0 0 0 4 0 0 4 1 0 0 0 0 4 0 2 2 1 0 0 0 0 4 the automorphism group has order 40 and is strongly generated by the following 3 elements: ( 4 0 0 0 4 0 2 2 1 , 1 0 0 2 3 0 0 0 3 , 4 3 0 3 4 0 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (3, 8), (2, 6, 5, 7), (1, 5, 2, 6) orbits: { 1, 6, 2, 7, 5 }, { 3, 8 }, { 4 } code no 42: ================ 1 1 1 4 0 0 0 0 2 1 0 0 4 0 0 0 3 1 0 0 0 4 0 0 2 2 1 0 0 0 4 0 3 3 1 0 0 0 0 4 the automorphism group has order 32 and is strongly generated by the following 4 elements: ( 4 0 0 0 4 0 3 3 1 , 2 0 0 0 2 0 3 3 4 , 4 3 0 3 4 0 0 0 2 , 1 1 2 0 0 3 4 3 0 ) acting on the columns of the generator matrix as follows (in order): (3, 8)(4, 7), (3, 4, 8, 7), (1, 5, 2, 6), (1, 7, 6, 3, 2, 4, 5, 8) orbits: { 1, 6, 8, 2, 7, 3, 4, 5 }