Guruswami, Li, Mosheiff, Resch, Silas and Wootters conjectured that, for every fixed prime power $q$ and $p\in(0,1-1/q)$, random linear codes of rate $1-h_q(p)-\varepsilon$ have list size $\frac{h_q(p)}{\varepsilon}\cdot(1+o(1))$ as $\varepsilon\to0$, both for list decoding and average-radius list decoding. The conject...
Local coordinate-wise linear (LCL) properties provide a unified framework for studying list decoding, list recovery and other local properties of linear codes. We prove that random one-point algebraic geometry (AG) codes have the same LCL threshold rates as random linear codes under explicit alphabet and sampling condi...
We prove that for every fixed prime power $q$, every $p\in(0,1-1/q)$, and every $\varepsilon>0$ with $1-H_q(p)-\varepsilon>0$, a random linear code over $\mathbb{F}_q$ of rate $1-H_q(p)-\varepsilon$ is $(p,\,\left\lceil\frac{H_q(p)}{\varepsilon}\right\rceil+O_{p,q}(1))\text{-list-decodable}$ with probability at least $...
Chen Yuan, Rui-Qi Zhu· 2 citations
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