Given a pair of finite groups $G$ and $H$, the set of homomorphisms from $G$ to $H$ form an error-correcting code where codewords differ in at least $1/2$ the coordinates. We show that for every pair of {\em abelian} groups $G$ and $H$, the resulting code is (locally) list-decodable from ... more >>>

We initiate the study of the role of erasures in local decoding and use our understanding to prove a separation between erasure-resilient and tolerant property testing. Local decoding in the presence of errors has been extensively studied, but has not been considered explicitly in the presence of erasures.

Motivated by ... more >>>

The original proof of the PCP Theorem composes a Reed-Muller-based PCP with itself, and then composes the resulting PCP with a Hadamard-based PCP [Arora, Lund, Motwani, Sudan and Szegedy ({\em JACM}, 1998)].
Hence, that proof applies a (general) proof composition result twice.
(Dinur's alternative proof consists of logarithmically many gap ... more >>>