New extremal self-dual codes of lengths 36, 38, and 58

We construct new extremal self-dual binary codes of lengths 36, 38, and 58. We show that there are at least 14 inequivalent extremal self-dual [38,18,8] codes and that there are at least 368 inequivalent extremal self-dual [38,19,8] codes. For length 58, we construct 11 extremal self-dual [58,29,10] codes whose weight enumerators were previously unknown