BIRS Workshop Lecture Videos
Constructing tree codes Cohen, Gil
In this talk, we consider the problem of explicitly constructing a binary tree code with constant distance and constant alphabet size. We present an explicit binary tree code with constant distance and alphabet size polylog(n), 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). For analyzing our construction, we prove a bound on the number of integral roots a real polynomial can have in terms of its sparsity with respect to the Newton basis - a result of independent interest.
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