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- W1555565700 abstract "In the present paper, we consider list decoding for both random rank metric codes and random linear rank metric codes. Firstly, we show that, for arbitrary $0<R<1$ and $epsilon>0$ ($epsilon$ and $R$ are independent), if $0<frac{n}{m}leq epsilon$, then with high probability a random rank metric code in $F_{q}^{mtimes n}$ of rate $R$ can be list-decoded up to a fraction $(1-R-epsilon)$ of rank errors with constant list size $L$ satisfying $Lleq O(1/epsilon)$. Moreover, if $frac{n}{m}geqTheta_R(epsilon)$, any rank metric code in $F_{q}^{mtimes n}$ with rate $R$ and decoding radius $rho=1-R-epsilon$ can not be list decoded in ${rm poly}(n)$ time. Secondly, we show that if $frac{n}{m}$ tends to a constant $bleq 1$, then every $F_q$-linear rank metric code in $F_{q}^{mtimes n}$ with rate $R$ and list decoding radius $rho$ satisfies the Gilbert-Varsharmov bound, i.e., $Rleq (1-rho)(1-brho)$. Furthermore, for arbitrary $epsilon>0$ and any $0<rho<1$, with high probability a random $F_q$-linear rank metric codes with rate $R=(1-rho)(1-brho)-epsilon$ can be list decoded up to a fraction $rho$ of rank errors with constant list size $L$ satisfying $Lleq O(exp(1/epsilon))$." @default.
- W1555565700 created "2016-06-24" @default.
- W1555565700 creator A5055926977 @default.
- W1555565700 date "2014-01-12" @default.
- W1555565700 modified "2023-09-27" @default.
- W1555565700 title "On List-decodability of Random Rank Metric Codes" @default.
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- W1555565700 doi "https://doi.org/10.48550/arxiv.1401.2693" @default.
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