A family of good uniquely decodable code pairs for the two-access binary adder channel

An explicit construction is presented of uniquely decodable code pairs for the two-access binary erasure channel. Through a computer search we found many code pairs coming from this construction with a rate pair above the nonconstructive lower bound known in the literature. Also presented is a simple uniquely decodable code pair, with a high rate pair, found by a different method.