Classification of Formally Self-Dual even Codes of Lengths up to 16

In this note, we give the complete classification of binary formally self-dual even codes of lengths 10, 12, 14 and 16. There are exactly fourteen, 29, 99 and 914 inequivalent such codes of lengths 10, 12, 14 and 16, respectively. This completes the classification of formally self-dual even codes of lengths up to 16. The first example of a formally self-dual even code with a trivial automorphism group is also found. This shows that 16 is the smallest length for which there is a formally self-dual even code with a trivial automorphism group.