An Alternative Decoding Method for Gabidulin Codes in Characteristic Zero
Gabidulin codes, originally defined over finite fields, are an important class of rank metric codes with various applications. Recently, their definition was generalized to certain fields of characteristic zero and a Welch--Berlekamp like algorithm with complexity $O(n^3)$ was given. We propose a ne...
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Zusammenfassung: | Gabidulin codes, originally defined over finite fields, are an important
class of rank metric codes with various applications. Recently, their
definition was generalized to certain fields of characteristic zero and a
Welch--Berlekamp like algorithm with complexity $O(n^3)$ was given. We propose
a new application of Gabidulin codes over infinite fields: low-rank matrix
recovery. Also, an alternative decoding approach is presented based on a Gao
type key equation, reducing the complexity to at least $O(n^2)$. This method
immediately connects the decoding problem to well-studied problems, which have
been investigated in terms of coefficient growth and numerical stability. |
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DOI: | 10.48550/arxiv.1601.05205 |