In the last few days, a Denial of Service attack was launched on universities in Israel, leading the administrators of the Israel Academic network to block access to it from the global internet. Consequently, websites such as ECCC have been accessible only from within the Israeli and European academic networks.
It seems that this blocking was just removed, and we hope it will not be put back in the future.
Needless to say, deciding on such blocking is not in our control, but we do apologize for this disruption of service.
We give new bounds for list sizes of random linear codes at capacity, max loads of linear hash functions, and Furstenberg sets, over every finite field $\mathbb{F}_q$.
1. Random linear codes over $\mathbb{F}_q$ with rate $1 - H_q(p) - \epsilon$ are $(p, O(q H_q(p)/\epsilon))$-list decodable with high probability for all ... more >>>
We prove that, for every constant $\varepsilon>0$ and every function $f:\Sigma^n\to\{0, 1\}$, there is a coalition of $O(n/\sqrt{\log n})$ coordinates and a target output $b\in\{0, 1\}$ such that, after the remaining coordinates are sampled uniformly and independently, the coalition can choose its values to make the output equal to $b$ ... more >>>
We prove that for all $\varepsilon>0$, there exists a positive integer $k$ such that given a $4$-to-$1$ Game $\Psi$ with alphabet size at most $k$, it is NP-hard to distinguish between the case that val$(\Psi)=1$ and the case that val$(\Psi)\leq \delta$. This confirms the $4$-to-$1$ Games Conjecture from [Khot, CCC ... more >>>
