A linear code is called self-orthogonal if it is contained in its dual. Self-orthogonal codes are theoretically interesting and have application to the construction of quantum error-correcting codes. They include self-dual codes which are closely related to combinatorial designs, secret sharing schemes, unimodular lattices, sphere packing, and groups.

In this talk, we introduce a series of recent papers on binary optimal self-orthogonal codes with small dimensions. In particular, we solve two conjectures on the largest minimum distance of a binary self-orthogonal code with dimension 5.