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- W2262313265 abstract "We show that decoding of $ell$-Interleaved Gabidulin codes, as well as list-$ell$ decoding of Mahdavifar--Vardy codes can be performed by row reducing skew polynomial matrices. Inspired by row reduction of $F[x]$ matrices, we develop a general and flexible approach of transforming matrices over skew polynomial rings into a certain reduced form. We apply this to solve generalised shift register problems over skew polynomial rings which occur in decoding $ell$-Interleaved Gabidulin codes. We obtain an algorithm with complexity $O(ell mu^2)$ where $mu$ measures the size of the input problem and is proportional to the code length $n$ in the case of decoding. Further, we show how to perform the interpolation step of list-$ell$-decoding Mahdavifar--Vardy codes in complexity $O(ell n^2)$, where $n$ is the number of interpolation constraints." @default.
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- W2262313265 date "2015-10-15" @default.
- W2262313265 modified "2023-09-27" @default.
- W2262313265 title "Row Reduction Applied to Decoding of Rank Metric and Subspace Codes" @default.
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