On the Structure of Cubic and Quartic Polynomials

@inproceedings{Haramaty2009OnTS,
  title={On the Structure of Cubic and Quartic Polynomials},
  author={Elad Haramaty and Amir Shpilka},
  booktitle={Electronic Colloquium on Computational Complexity},
  year={2009}
}
In this paper we study the structure of polynomials of degree three and four that have high bias or high Gowers norm, over arbitrary prime fields. In particular we obtain the following results. 1. We give a canonical representation for degree three or four polynomials that have a significant bias (i.e. they are not equidistributed). This result generalizes the corresponding results from the theory of quadratic forms. This significantly improves previous results for such polynomials. 2. For the… CONTINUE READING