Self-dual codes from quotient matrices of symmetric divisible designs with the dual property

Abstract

In this paper we look at codes spanned by the rows of a quotient matrix of a symmetric (group) divisible design (SGDD) with the dual property. We define an extended quotient matrix and show that under certain conditions the rows of the extended quotient matrix span a self-dual code with respect to a certain scalar product. We also show that sometimes a chain of codes can be used to associate a self-dual code to a quotient matrix of a SGDD with the dual property.