A new method for constructing small-bias spaces from Hermitian codes

TL;DR

This paper introduces a novel construction method for small-bias spaces using Hermitian codes, offering faster construction times and improved performance over existing norm-trace code-based spaces.

Contribution

The paper presents a new, efficient method for constructing small-bias spaces leveraging Hermitian codes, outperforming traditional algebraic geometric and norm-trace code methods.

Findings

Faster construction of small-bias spaces for certain parameters

Improved bias properties compared to norm-trace code-based spaces

Competitive speed and performance in relevant parameter regions

Abstract

We propose a new method for constructing small-bias spaces through a combination of Hermitian codes. For a class of parameters our multisets are much faster to construct than what can be achieved by use of the traditional algebraic geometric code construction. So, if speed is important, our construction is competitive with all other known constructions in that region. And if speed is not a matter of interest the small-bias spaces of the present paper still perform better than the ones related to norm-trace codes reported in [12].