The paper focuses on the communication complexity of multiplying elements from the group H = SL(2, q) in the number-on-forehead model with k parties. The authors prove a lower bound of (t log H)/ck, which is an exponential improvement over previous work and matches the state-of-the-art in the area.
Relatedly, the authors show that the convolution of kc independent copies of a 3-uniform distribution over Hm is close to a k-uniform distribution, again an exponential improvement over previous work which needed ck copies. The proofs are remarkably simple and the results extend to other quasirandom groups.
The authors also generalize previous work on the relationship between (ϵ, k)-uniformity and k-uniformity, showing that any distribution over Hm whose weight-k Fourier coefficients are small is close to a k-uniform distribution. This proof is simpler than previous work in the abelian setting.
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arxiv.org
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by Harm Derksen... : arxiv.org 09-12-2024
https://arxiv.org/pdf/2409.06932.pdfDaha Derin Sorular