The Existence of a Self-Dual [70, 35, 12] Code and Formally Self-Dual Codes

In this note, the existence of self-dual codes and formally self-dual even codes is investigated. A construction for self-dual codes is presented, based on extending generator matrices. Using this method, a singly-even self-dual [70, 35, 12] code is constructed from a self-dual code of length 68. This is the first published example of a singly-even [70, 35, 12] code. Constructions are also given for formally self-dual even codes. Extremal formally self-dual even codes are constructed.