Building on work of Yekhanin and Raghavendra, Efremenko recently gave an elegant construction of 3-query LDCs which achieve sub-exponential length unconditionally. In this note, we observe that this construction can be viewed in the framework of Reed-Muller codes.

A crucial ingredient in these codes is the construction of a large family of matching verctors. We present a simple and elegant construction due to Sudan which matches the best known construction.