ON SELF-DUAL AFFINE-INVARIANT CODES

An extended cyclic code of length 2m over GF(2) cannot be self-dual for even m. For odd m, the Reed-Muller code [2m, 2m-1, 2(m+1)/2] is affine-invariant and self-dual, and it is the only such code for m = 3 or 5. We describe the set of binary self-dual affine-invariant codes of length 2m for m = 7 and m = 9. For each odd m, m greater-than-or-equal-to 9, we exhibit a self-dual affine-invariant code of length 2m over GF(2) which is not the self-dual Reed-Muller code. In the first part of the paper, we present the class of self-dual affine-invariant codes of length 2rm over GF(2r), and the tools we apply later to the binary codes. (C) 1994 Academic Press, Inc.