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

In this paper we present a modification of Reed-Solomon codes that beats the GuruwamiSudan 1− √ R decoding radius of Reed-Solomon codes at low rates R. The idea is to choose Reed-Solomon codes U and V with appropriate rates in a (U | U + V ) construction and to decode them with the Koetter-Vardy soft information decoder. We suggest to use a slightly more general version of these codes (but which has the same decoding performances as the (U | U + V )-construction) for code-based cryptography, namely to build a McEliece scheme. The point is here that these codes not only perform nearly 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 a previous McEliece proposal based on generalized Reed-Solomon codes.