We introduce a class of polynomials, which we call U-polynomials, and show that the problem of explicitly constructing a rigid matrix can be reduced to the problem of explicitly constructing a small hitting set for this class. We prove that small-bias sets are hitting sets for the class of U-polynomials, though their size is larger than desired. Furthermore, we give two alternative proofs for the fact that small-bias sets induce rigid matrices. Finally, we construct rigid matrices from unbalanced expanders, with essentially the same size as the construction via small-bias sets.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computational Theory and Mathematics
- Computational Mathematics
- Matrix rigidity
- small-bias sets
- unbalanced expanders