A win-win reduction from worst-case decoding and distinguishing problems yields average-case LPN hardness at noise rate n to the minus alpha for any constant alpha less than 1.
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Towards Worst-case Hardness for Low-Noise LPN
A win-win reduction from worst-case decoding and distinguishing problems yields average-case LPN hardness at noise rate n to the minus alpha for any constant alpha less than 1.