New MDS self-dual codes over finite fields of $F_{r^2}$

In recent years, many MDS self-dual codes with new lengths have been constructed. The main method is to obtain a new structure by generalized Reed-Solomon codes. In this paper, combined with [20], our constructions take up a proportion of generally more than 57% in all the possible lengths of $q$-ary MDSself-dual codes, which is larger than the previous results.