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In this paper we present a modification of Reed-Solomon codes that beats theGuruwami-Sudan $1-\sqrt{R}$ decoding radius of Reed-Solomon codes at low rates$R$. The idea is to choose Reed-Solomon codes $U$ and $V$ with appropriaterates in a $\left( U\mid U+V\right)$ construction and to decode them with theKoetter-Vardy soft information decoder. We suggest to use a slightly moregeneral version of these codes (but which has the same decoding performances asthe $\left( U\mid U+V\right)$-construction) for code-based cryptography, namelyto build a McEliece scheme. The point is here that these codes not only performnearly as well (or even better in the low rate regime) as Reed-Solomon codes,their structure seems to avoid the Sidelnikov-Shestakov attack which broke aprevious McEliece proposal based on generalized Reed-Solomon codes.

Using Reed-Solomon codes in the $\left( U\mid U+V\right)$ construction and an application to cryptography