Article at Quanta, but here's the TLDR infographic that gets to the nitty-gritty:
Why do all this? Chiefly transmission error detection & correction without having to send overly-redundant data. Additionally, as a component in encryption seems to be an equally useful byproduct.
I'd always wondered about these things, they being not generally in my particular thicket of the physics-and-math woods. Explanations usually took the form of "you know, REED-SOLOMON CODES, everyone knows about them, sheesh" or "here's a semester's worth of linear algebra to ponder, after which the point will become transparent." It's good to have a comprehensible short version.
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