Courtois-Finiasz-Sendrier (CFS) digital signatures critically depend on the ability to efficiently find a decodable syndrome by random sampling the syndrome space, previously restricting the class of codes upon which they could be instantiated to generic binary Goppa codes. In this paper we show how to construct t-error correcting quasi-dyadic codes where the density of decodable syndromes is high, while also allowing for a reduction by a factor up to t in the key size.