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About this paper
Songsong Li, Chaoping Xing, Chen Yuan, Ruiqi Zhu
The authors extend proximity and correlated agreement guarantees from Reed–Solomon codes to one-point algebraic-geometric codes. Below half the designed distance, their theorem bounds the fraction of close random combinations needed to force shared-coordinate approximations. For affine lines, fixed rate, and positive slack, this bound is O(2/(εq)), independent of block length; the guarantee applies only under these radius and field conditions.
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