We describe a new family of symmetric error-correcting codes with low-density parity-check matrices (LDPC).

Our codes can be described in two seemingly different ways. First, in relation to Reed-Muller codes: our codes are functions on a subset of $\mathbb{F}^n$ whose restrictions to a prescribed set of affine lines has low ... more >>>

We prove hypercontractive inequalities on high dimensional expanders. As in the settings of the p-biased hypercube, the symmetric group, and the Grassmann scheme, our inequalities are effective for global functions, which are functions that are not significantly affected by a restriction of a small set of coordinates. As applications, we ... more >>>