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Parchive 2 was, I believe, an implementation of Reed-Solomon at the application level; mostly used (when it was introduced) to counter loss from missing chunks on binary newsgroups. I think RAR might have picked up a similar feature around that time too?

I believe parchive version 1 was simple XOR parity.

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No, parchive v1 also used Reed-Solomon. The main difference between v1 and v2 was that v1 worked on the file level, but v2 divided the set of files into blocks.

Also, the parity matrix for v1 would be sometimes singular (non-invertible), which v2 tried to fix but it didn't quite work.

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