94B05 94B15 3 self-dual codes 3 05E20 2 11H31 2 11T23 2 11T71 2 20C05 2 20G40 2 22D20 2 Generalized Reed--Muller code 2 Golay codes 2 Index terms-recursive formula 2 Reed--Muller code 2 \(\mathbb{Z}_q\)-linear code 2 \(\mathbb{Z}_q\)-simplex code, 2 codes over fields 2 codes over finite rings 2 extended binary codes 2 group algebra 2 group ring codes 2 monomial equivalence 2 multi-dimensional Kloosterman sum, 2 nilpotent groups 2 radical 2 self-dual code; group algebra; Jacobson radical 2 03G10 1 13B05 1 16P10 1 94B25 1