Formally self-dual additive codes over F4

Additive codes over F4 have been of great interest due to their application to quantum error correction. As another application, we introduce a new class of formally self-dual additive codes over F4, which is a natural analogue of the binary formally self-dual codes and is missing in the study of additive codes over F4. In fact, Gulliver and Östergård (2003), considered formally self-dual linear codes over F4 of even lengths, and Choie and Solé (2008) suggested classifying formally self-dual linear codes over F4 of odd lengths in order to study lattices from these codes. These motivate our study on formally self-dual additive codes over F4. In this paper, we define extremal and near-extremal formally self-dual additive codes over F4, classify all extremal codes, and construct many near-extremal codes. We discuss a general method (called the weak balance principle) for constructing such codes. We conclude with some open problems.