On a construction of self-orthogonal codes from orbit matrices of 2-designs

In 2003, Harada and Tonchev presented a construction of self-orthogonal codes from orbit matrices of symmetric $2$-designs with fixed point free automorphisms. Since then, the constructions of self-orthogonal codes from orbit matrices of $2$-designs has been extensively studied. In this paper, we present new constructions of self-orthogonal codes from orbit matrices of $2$-designs for the cases not covered by the previously described methods. We construct self-orthogonal codes from orbit matrices of $2$-$(1024,496,249)$ and $2$-$(45,5,1)$ designs. Some of the constructed codes are optimal.