Pseudorandom linear codes are list decodable to capacity

AL Putterman, E Pyne - arXiv preprint arXiv:2303.17554, 2023 - arxiv.org
We introduce a novel family of expander-based error correcting codes. These codes can be
sampled with randomness linear in the block-length, and achieve list-decoding capacity …

Threshold rates of code ensembles: Linear is best

N Resch, C Yuan - IEEE Transactions on Information Theory, 2024 - ieeexplore.ieee.org
In this work, we prove new results concerning the combinatorial properties of random linear
codes. By applying the thresholds framework from Mosheiff et al.(FOCS 2020) we derive fine …