Extended maximal self-orthogonal codes

Self-dual and maximal self-orthogonal codes over [Formula: see text], where [Formula: see text] is even or [Formula: see text](mod 4), are extensively studied in this paper. We prove that every maximal self-orthogonal code can be extended to a self-dual code as in the case of binary Golay code. Using these results, we show that a self-dual code can also be constructed by gluing theory even if the sum of the lengths of the gluing components is odd. Furthermore, the (Hamming) weight enumerator [Formula: see text] of a self-dual code [Formula: see text] is given in terms of a maximal self-orthogonal code [Formula: see text], where [Formula: see text] is obtained by the extension of [Formula: see text].