What are the advantages of coding based cryptosytems over LWE (Regev)?

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Having recently learned of coding based cryptography, it seems that they key size for post-quantum security might be a lot larger than what is required by Regev PKE (in the former keys include several large matrices), which is also post-quantum secure. Is this a correct observation? Ether way - what are the pros and cons of these two methods?

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TL;DR codes: Public keys for code-based are large (McEliece is huge, key generation takes a long while). Some other code schemes use more structured codes to reduce key size. Encryption is fast and ciphertexts are small. Try looking at Appendix D of for some numerical comparisons.
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