Recently, Cohen, Haeupler and Schulman gave an explicit construction of binary tree codes over polylogarithmic-sized output alphabet based on Pudl{a}ks construction of maximum-distance-separable (MDS) tree codes using totally-non-singular triangular matrices. In this short note, we give a unified and simpler presentation of Pudl{a}k and Cohen-Haeupler-Schulmans constructions.
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