Extremal doubly-even self-dual cocyclic [40,20] codes

The structure of cocyclic Hadamard matrices allows us a much faster and more systematic search for binary, self-dual codes. The search for binary self-dual [40,20] codes from Z₅×Z₂²-cocyclic Hadamard matrices and two types of D₂₀-cocyclic Hadamard matrices resulted in 25 equivalence classes of extremal doubly-even codes. It is worth noting that the equivalence classes found in each case were disjoint, emphasising the importance of the cocyclic structure of the Hadamard matrices used