the 1 isometry classes of irreducible [23,14,5]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 1 elements: ( 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (1, 23, 9, 21)(2, 6, 18, 12)(3, 16, 11, 10)(4, 15, 5, 17)(7, 22, 20, 8) orbits: { 1, 21, 9, 23 }, { 2, 12, 18, 6 }, { 3, 10, 11, 16 }, { 4, 17, 5, 15 }, { 7, 8, 20, 22 }, { 13 }, { 14 }, { 19 }