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A full mathematical explanation and working code: https://www.nayuki.io/page/reed-solomon-error-correcting-cod... , https://news.ycombinator.com/item?id=13565939
My understanding was that noone really use these nowadays for networks as error codes are cheaper and you can just retransmit if there’s an error. But maybe RS is still used for storage memory?
In any case it’s used massively in zero-knowledge proofs to construct all sorts of hash-based schemes (see FRI, ligero, fractal, vortex, etc.)
RS and other forward error correction codes are used in everything now. It's in Ethernet, USB (4.0), and PCIe (6.0) for starters. Every kind of link is being pushed to the absolute limit, and you can usually trade performance for a higher bit error rate, and then fix the errors with FEC. Now that the silicon to encode/decode RS is fast, it goes everywhere.
Backblaze (cloud backup/storage) uses Reed Solomon encodings.
RS is used in distributed storage system like hadoop for fault-tolerance
https://hadoop.apache.org/docs/r3.4.0/hadoop-project-dist/ha...
Erasure Coding is ubiquitous in storage, for instance in MinIO or Ceph. Usually that means Reed-Solomon.