Block-Accumulate Codes: Accelerated Linear Codes for PCGs and ZK

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Linear error-correcting codes with fast encoding and high minimum distance are a central primitive across modern cryptography. They appear prominently in at least two domains: (1) pseudorandom correlation generators (PCGs), which enable sublinear-communication generation of correlations such as oblivious transfer and vector oblivious linear evaluation, and (2) zero-knowledge proof systems, where linear-time encoders underpin proof soundness and scalability. In both settings, the prover or sender