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 show that Reed-Solomon codes of dimension $k$ and block length $n$ over any finite field $\mathbb{F}$ can be deterministically list decoded from agreement $\sqrt{(k-1)n}$ in time $\text{poly}(n, \log |\mathbb{F}|)$.
Prior to this work, the list decoding algorithms for Reed-Solomon codes, from the celebrated results of ...
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This paper is about the proximity gaps phenomenon for Reed-Solomon codes.
Very roughly, the proximity gaps phenomenon for a code $\mathcal C \subseteq \mathbb F_q^n$ says that for two vectors $f,g \in \mathbb F_q^n$, if sufficiently many linear combinations $f + z \cdot g$ (with $z \in \mathbb F_q$) ...
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A large alphabet Locally Decodable Code (LDC) $C:\Sigma^{k} \to \Sigma'^{n}$, where $\Sigma'$ may be large, is a code where each symbol of $x$ can be decoded by making few queries to a noisy version of $C(x)$. The rate of $C$ is its information rate, namely $\frac{k \log (|\Sigma|) }{n \log ... more >>>
