Extremal ternary self-dual codes of length 36 and symmetric 2-(36, 15, 6) designs with an automorphism of order 2

In this note, we report the classification of all symmetric 2-(36, 15, 6) designs that admit an automorphism order 2 and their incidence matrices generate extremal ternary self-dual code. It is shown up to isomorphism, there exists only one such design, having a full group 24, code spanned by its matrix equivalent Pless symmetry