A definition of a self-dual code on graph and a procedure based on factor graphs to judge a self-dual code were presented. Three contributions of this paper were described as follows. To begin with, transform TR→L were defined, which was the basis of self-dual codes defined on graphs and played a key role in the paper. The second were that a self-dual code could be defined on factor graph, which was much different from conventional algebraic method. The third was that a factor graph approach to judge a self-dual code was illustrated, which took advantage of duality properties of factor graphs and our proposed transform TR→L to offer a convenient and geometrically intuitive process to judge a self-dual code.
