We consider FrodoKEM, a lattice-based cryptosystem based on LWE, and propose
a new error correction mechanism to improve its performance. Our encoder maps
the secret key block-wise into the Gosset lattice $E_8$. We propose two sets of
parameters for our modified implementation. Thanks to the improved error
correction, the first implementation outperforms FrodoKEM in terms of concrete
security by $10$ to $13$ bits by increasing the error variance; the second
allows to reduce the bandwidth by $7%$ by halving the modulus $q$. In both
cases, the decryption failure probability is improved compared to the original
FrodoKEM. Unlike some previous works on error correction for lattice-based
protocols, we provide a rigorous error probability bound by decomposing the
error matrix into blocks with independent error coefficients.

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