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Article overview
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A Basis for all Solutions of the Key Equation for Gabidulin Codes | | Antonia Wachter
; Vladimir Sidorenko
; Martin Bossert
; | | Date: |
9 Jun 2010 | | Abstract: | We present and prove the correctness of an efficient algorithm that provides
a basis for all solutions of a key equation in order to decode Gabidulin (G-)
codes up to a given radius tau. This algorithm is based on a symbolic
equivalent of the Euclidean Algorithm (EA) and can be applied for decoding of
G-codes beyond half the minimum rank distance. If the key equation has a unique
solution, our algorithm reduces to Gabidulin’s decoding algorithm up to half
the minimum distance. If the solution is not unique, we provide a basis for all
solutions of the key equation. Our algorithm has time complexity O(tau^2) and
is a generalization of the modified EA by Bossert and Bezzateev for
Reed-Solomon codes. | | Source: | arXiv, 1006.1743 | | Services: | Forum | Review | PDF | Favorites | |
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