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Gabidulin codes can be seen as the rank-metric equivalent of Reed-Solomon codes. It was recently proven, using subspace polynomials, that Gabidulin codes cannot be list decoded beyond the so-called Johnson radius. In another result, cyclic subspace codes were constructed by inspecting the connection between subspaces and their subspace polynomials. In this paper, these subspace codes are used to prove...
Codes in rank metric have a wide range of applications. To construct such codes with better list-decoding performance explicitly, it is of interest to investigate the list-decodability of random rank metric codes. It is shown that if $n/m=b$ is a constant, then for every rank metric code in $ {\mathbf {F}}_{q}^{m\times n}$ with rate $R$ and list-decoding radius $\rho $ must obey the Gilbert–Varshamov...
Our aim is to present a new construction of network coding from algebraic curves over finite fields. Moreover, the Reed-Solomon-like code construction introduced by Ralf Kotter in his paper coding for errors and erasures in random network coding is one simple case of our construction.
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