The Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP) are the fundamental algorithmic questions in the geometry of numbers. In the past two decades, their algorithmic complexity has been studied quite extensively due to their connection with lattice based cryptosystems. In this paper, we study these problems in ... more >>>

We give a unified hidden-derivative framework for list decoding and mutual correlated agreement of ordinary Reed--Solomon codes over prime fields, on arbitrary prescribed evaluation sets. For every fixed slack $\gamma>0$, every sufficiently large block length $n$, every prime $q\ge n$, and every dimension $1\le k\le(1-\gamma)n$, a deterministic algorithm finds all ... more >>>

Guo and Wang gave a deterministic polynomial-time black-box identity test for $\Sigma^{[3]}\Pi\Sigma\Pi^{[\delta]}$ circuits over fields of arbitrary characteristic, for constant $\delta$, assuming that one product gate is squarefree. This note communicates an observation suggested by a large language model: the squarefreeness assumption can be removed by combining the normalization argument ... more >>>