Codes from Symmetry Groups, and a [32, 17, 8] Code

Let G be the automorphism group of the four-dimensional cube, a group of order24 . 4 ! = 384. The binary codes associated with the 32-dimensional permutationrepresentation of G on the edges of the cube are investigated. There are about 400 suchcodes, one of which is a [32, 17, 8] code, having twice as many codewords as the[32, 16, 8] extended quadratic residue code. __________* This paper appeared in SIAM J. Discrete Math., vol. 2 (1989), pp. 28–37.** Present address: AT&T; Bell Laboratories, Holmdel, NJ 07733.