Recursive decoding of binary rank Reed-Muller codes and Plotkin construction for matrix codes
Résumé
We give a recursive decoding algorithm of the rank metric Reed-Muller codes introduced by Augot, Couvreur, Lavauzelle and Neri in 2021 for the binary case, i.e., $G = (\mathbb{Z}/{2\mathbb{Z}})^m$. In a broad range of parameters, this recursive decoding algorithm has better complexity compared to a recently proposed decoding algorithm based on Dickson matrices. Imitating the recursive structure, we introduce a Plotkin-like construction of matrix rank metric codes over finite fields and provide a decoding algorithm associated to this construction.
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