A Probabilistic Lower Bound on the Max- imum Size of a List-of-Two Decodable Code

List decoding of block codes is a decoding strategy which potentially allows better utilization of the error-correction capability of the code being decoded than traditional decoding up to half the minimum distance of the code. The basic idea dates back to 1957 but has fairly recently been the object of renewed interest from the research community, after the development of efficient algorithms for list decoding of the much used Reed-Solomon codes. In this paper we investigate general lower bounds on the maximum size of a (τ, 2)-list-decodable q-ary code. We identify some basic lower bounds based on classic general lower bounds on the maximum size of a code with given minimum distance. We also present a more complicated bound based on a non-constructive, probabilistic approach which improves on the basic bounds for some cases.