An Alternative Decoding Method for Gabidulin Codes in Characteristic Zero [article]

Sven Müelich and Sven Puchinger and David Mödinger and Martin Bossert
2016 arXiv   pre-print
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
more » ... 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.
arXiv:1601.05205v2 fatcat:alqqhr7mp5a23a4x6zvcp3zi4q