Explicit, almost optimal, epsilon-balanced codes

@article{TaShma2017ExplicitAO,
  title={Explicit, almost optimal, epsilon-balanced codes},
  author={Amnon Ta-Shma},
  journal={Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing},
  year={2017}
}
  • A. Ta-Shma
  • Published 19 June 2017
  • Computer Science
  • Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing
The question of finding an epsilon-biased set with close to optimal support size, or, equivalently, finding an explicit binary code with distance 1-ϵ/2 and rate close to the Gilbert-Varshamov bound, attracted a lot of attention in recent decades. In this paper we solve the problem almost optimally and show an explicit ϵ-biased set over k bits with support size O(k/ϵ2+o(1)). This improves upon all previous explicit constructions which were in the order of k2/ϵ2, k/ϵ3 or k5/4/ϵ5/2. The result is… 
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