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    Noisy polynomial interpolation modulo prime powers

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    We consider the {\it noisy polynomial interpolation problem\/} of recovering an unknown ss-sparse polynomial f(X)f(X) over the ring Zpk\mathbb Z_{p^k} of residues modulo pkp^k, where pp is a small prime and kk is a large integer parameter, from approximate values of the residues of f(t)∈Zpkf(t) \in \mathbb Z_{p^k}. Similar results are known for residues modulo a large prime pp, however the case of prime power modulus pkp^k, with small pp and large kk, is new and requires different techniques. We give a deterministic polynomial time algorithm, which for almost given more than a half bits of f(t)f(t) for sufficiently many randomly chosen points t∈Zpkβˆ—t \in \mathbb Z_{p^k}^*, recovers f(X)f(X)
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