Before revision:  In this work, we provide an algorithm that learns the distribution using only \exp\big(O(n^{1/3}) \cdot \ell^2\big) samples, by developing a higher-moment analog of the algorithms of [DOS17, NP17] \big(O)}\big)  .
After revision:  In this work, we provide an algorithm that learns the distribution using only \exp\big(O(n^{1/3}) \cdot \ell^2\big) samples, by developing a higher-moment analog of the algorithms of [DOS17, NP17] , which solve trace reconstruction in \exp\big(O)}\big) .