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Technical Program

Paper Detail

Paper IDD1-S1-T2.2
Paper Title Efficient Decoding of Gabidulin Codes over Galois Rings
Authors Sven Puchinger, Technical University of Denmark, Denmark; Julian Renner, Antonia Wachter-Zeh, Technical University of Munich, Germany; Jens Zumbrägel, University of Passau, Germany
Session D1-S1-T2: Rank-Metric Codes I
Chaired Session: Monday, 12 July, 22:00 - 22:20
Engagement Session: Monday, 12 July, 22:20 - 22:40
Abstract 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.