|| Efficient Decoding of Gabidulin Codes over Galois Rings
||Sven Puchinger, Technical University of Denmark, Denmark; Julian Renner, Antonia Wachter-Zeh, Technical University of Munich, Germany; Jens Zumbrägel, University of Passau, Germany|
||D1-S1-T2: Rank-Metric Codes I
||Monday, 12 July, 22:00 - 22:20
||Monday, 12 July, 22:20 - 22:40
This paper presents the first decoding algorithm for Gabidulin codes over Galois rings with provable quadratic complexity in the code length. The new method consists of two steps: (1) solving a syndrome-based key equation to obtain the annihilator polynomial of the error and therefore the column space of the error, (2) solving a key equation based on the received word in order to reconstruct the error vector. This two-step approach became necessary since standard solutions as the Euclidean algorithm do not properly work over rings.