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A basis for all solutions of the key equation for Gabidulin codes
By: Bossert, M.; Sidorenko, V.; Wachter, A.;
2010 / IEEE / 978-1-4244-7892-7
This item was taken from the IEEE Conference ' A basis for all solutions of the key equation for Gabidulin codes ' 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 � 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(�sup>2) and is a generalization of the modified EA by Bossert and Bezzateev for Reed-Solomon codes.