On the asymptotic number of inequivalent binary self-dual codes

Let Ψ n be the number of inequivalent self-dual codes in F 2 2 n . We prove that lim n → ∞ ( 2 n ) ! τ 2 − 1 2 n ( n − 1 ) Ψ n = 1 , where τ = ∏ j = 1 ∞ ( 1 + 2 − j ) ≈ 2.38423 . Let Δ n be the number of inequivalent doubly even self-dual codes in F 2 8 n . We also prove that lim n → ∞ ( 8 n ) ! τ 2 − 2 n ( 4 n − 3 ) Δ n = 1 .