Hadamard matrices of order 32 and extremal ternary self-dual codes

As described in [7], self-dual codes are an important class of linear codes for both theoretical and practical reasons. It is a fundamental problem to classify self-dual codes of modest length and determine the largest minimum weight among self-dual codes of that length (see [7]). By the Gleason–Pierce theorem, there are nontrivial divisible self-dual codes over Fq for q = 2, 3 and 4 only, where Fq denotes the finite field of order q (see [7, Theorem 5]), and