For an abelian topological group G, let Ĝ denote the dual group of all continuous characters endowed with the compact open topology. Given a closed subset X of an infinite compact abelian group G such that w(X) < w(G), and an open neighbourhood U of 0 in T, we show that |{χ ∈ Ĝ : χ(X) ⊆ U}| = |Ĝ|. (Here, w(G) denotes the weight of G.) A subgroup D of G determines G if the map r : Ĝ → D̂ defined ...

The McEliece cryptosystem is one of the few systems to be considered secure against attacks by Quantum computers. The original scheme is built upon Goppa codes and produces very large keys, hence recent research has focused mainly on trying to reduce the public key size. Previous proposals tried to replace the class of Goppa codes with other families of codes, but this was revealed to be an ins...