the 3 isometry classes of irreducible [5,2,4]_16 codes are: code no 1: ================ 1 1 1 1 0 3 2 1 0 1 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 15 0 0 15 15 15 0 0 15 , 2 , 12 12 12 0 0 12 0 12 0 , 0 , 0 14 0 14 0 0 14 14 14 , 0 ) acting on the columns of the generator matrix as follows (in order): (2, 4), (1, 4)(2, 3), (1, 2)(3, 4) orbits: { 1, 4, 2, 3 }, { 5 } code no 2: ================ 1 1 1 1 0 5 2 1 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 2 12 10 0 0 8 0 14 0 , 2 , 0 0 2 15 0 0 7 8 10 , 1 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(2, 3), (1, 2, 5, 3) orbits: { 1, 5, 3, 2 }, { 4 } code no 3: ================ 1 1 1 1 0 11 10 1 0 1 the automorphism group has order 240 and is strongly generated by the following 7 elements: ( 3 0 0 0 3 0 0 0 3 , 2 , 15 0 0 0 2 0 0 0 13 , 1 , 6 0 0 0 6 0 6 6 6 , 1 , 6 0 0 6 6 6 0 6 0 , 2 , 0 0 6 0 6 0 6 0 0 , 1 , 11 11 11 0 0 11 11 0 0 , 1 , 13 2 15 2 0 0 15 15 15 , 0 ) acting on the columns of the generator matrix as follows (in order): id, (4, 5), (3, 4), (2, 3, 4), (1, 3), (1, 3, 2, 4), (1, 2, 4, 3, 5) orbits: { 1, 3, 4, 5, 2 }