Constructing Small-Bias Sets from Algebraic-Geometric Codes

We give an explicit construction of an ϵ-biased set over k bits of size O(k/ϵ2log(1/ϵ))5/4. This improves upon previous explicit constructions when ϵ is roughly (ignoring logarithmic factors) in the range [k−1.5,k−0.5]. The construction builds on an algebraic geometric code. However, unlike previous constructions, we use low-degree divisors whose degree is significantly smaller than the genus.