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

Authors:
Olav Geil;Stefano Martin;Ryutaroh Matsumoto
Affiliations:
Department of Mathematical Sciences, Aalborg University, Denmark;Department of Mathematical Sciences, Aalborg University, Denmark;Department of Mathematical Sciences, Aalborg University, Denmark, Department of Communications and Integrated Systems, Tokyo Institute of Technology, Japan
Venue:
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
Year:
2012

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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].