On Lattices, Learning with Errors, Random Linear Codes ...

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m, for any other word s0, the Hamming distance of t from Qs0 is roughly m(1 ¡ 1=p). Hence, we obtain that approximating the nearest codeword problem to within factors smaller than (1 ¡ 1=p)=(1 ¡ 1=(fip)) on random codes is as hard as quantumly approximating worst-case lattice problems. This gives a partial

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