Self-dual codes from extended orbit matrices of symmetric designs

In this paper we study codes spanned by the rows of an orbit matrix of a symmetric design with respect to the action of an automorphism group that acts with all orbits of the same length. We define an extended orbit matrix and show that under some condition the rows of the extended orbit matrix span a code that is self-dual with respect to a certain scalar product. Further, we show that sometimes a chain of codes can be used to associate a self-dual code to an orbit matrix of a symmetric design.