Some relevant additional detail from NIST's paper selecting HQC..

On Thursday, 13 March 2025 10:01 UTC, Alicja Kario wrote:
> NIST has selected HQC for standardisation this week... No idea about
> its patent situation, or if we want something with ciphertexts this big in
> TLS... (reminder: 4.4 kiB, 8.8 kiB, and 14.1 kiB for 128, 192 and 256
> bit level of security respectively)

As well as HQC's selection, NIST also called out Classic McEliece in their
report as a possible future NIST standard once ISO/IEC is finished with it:
See https://nvlpubs.nist.gov/nistpubs/ir/2025/NIST.IR.8545.pdf
> In the event that Classic McEliece does become widely
> used through other standards, and that NIST remains confident in its
security while also
> determining that there is sufficient need, NIST may develop a NIST
standard based on the
> widely used version.

It has better ciphertext sizes, but much much worse
encapsulation/decapsulation key sizes.

Andrew Scott
https://aes.id.au/
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