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Electronic Colloquium on Computational Complexity

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TR22-075 | 21st May 2022
Siddharth Bhandari, Prahladh Harsha, Ramprasad Saptharishi, Srikanth Srinivasan

Vanishing Spaces of Random Sets and Applications to Reed-Muller Codes

Revisions: 1

We study the following natural question on random sets of points in $\mathbb{F}_2^m$:

Given a random set of $k$ points $Z=\{z_1, z_2, \dots, z_k\} \subseteq \mathbb{F}_2^m$, what is the dimension of the space of degree at most $r$ multilinear polynomials that vanish on all points in $Z$?

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