Error Correcting Codes, finding polynomials of bounded degree agreeing on a dense fraction of a set of points

TL;DR

This paper revises and improves a randomized algorithm by Sudan for efficiently finding low-degree polynomials that agree with a dense subset of points over a finite field.

Contribution

It provides revised arguments and enhancements to Sudan's algorithm for polynomial recovery in the context of error-correcting codes.

Findings

Revised the probabilistic analysis of Sudan's algorithm.

Improved bounds on the density of points for successful polynomial recovery.

Enhanced understanding of polynomial agreement in finite fields.

Abstract

Here we present some revised arguments to a randomized algorithm proposed by Sudan to find the polynomials of bounded degree agreeing on a dense fraction of a set of points in $\mathbb{F}^{2}$ for some field $\mathbb{F}$.