Eulerian Self-Dual Codes
László Babai, Haluk Oral, Kevin T. Phelps · SIAM Journal on Discrete Mathematics · 1994
The authors present a construction of binary self-dual codes from Eulerian graphs and establish that the code will be indecomposable if and only if the vertices of degree 2 are not a cutset of the graph. The construction is used to establish that every finite group is isomorphic to the automorphism group of some self dual code. It is further shown that deciding isomorphism of self-dual codes is at least as difficult as graph isomorphism.