New extremal self-dual codes of lengths 36 and 38

There are two distinct weight enumerators for extremal singly-even self-dual [36, 18, 8] codes. For each weight enumerator, only one extremal self-dual code is previously known. In this correspondence, we construct several new extremal singly-even self dual [36, 18, 8] codes for each weight enumerator. We also construct a number of new extremal singly-even self-dual [38, 19, 8] codes.