Explicit Binary Tree Codes with Polylogarithmic Size Alphabet.

This paper makes progress on the problem of explicitly constructing a binary tree code with constant distance and constant alphabet size. We give an explicit binary tree code with constant distance and alphabet size poly(logn), where n is the depth of the tree. This is the first improvement over a two-decade-old construction that has an exponentially larger alphabet of size poly(n). At the core of our construction is the first explicit tree code with constant rate and constant distance, though with non-constant arity - a result of independent interest. This construction adapts the polynomial interpolation framework to the online setting.