WEIGHT POLYNOMIALS OF SELF-DUAL CODES AND THE MacWILLIAMS IDENTITIES
Andrew M. Gleason · 1970
Many error correcting codes are known to be self-dual. Hence the MacWilliams identities put a considerable restriction on the possible weight distribution of such a code. We show that this restriction, for codes over GF(2) and GF(3), is that the weight polynomial must lie in an explicitly described free polynomial ring. To extend these results (in part) to self-dual codes over larger fields, we introduce more general weight polynomials and extend the MacWilliams identities to these.