Volume 9 (2013) Article 5 pp. 253-272
Constructing Small-Bias Sets from Algebraic-Geometric Codes
Revised: October 29, 2012
Published: February 20, 2013
We give an explicit construction of an $\eps$-biased set over $k$ bits of size $O\left(\frac{k}{\eps^2 \log(1/\eps)}\right)^{5/4}$. This improves upon previous explicit constructions when $\eps$ 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.