Efficient Decoding of Gabidulin Codes over Galois Rings

Sven Puchinger, Julian Renner, Antonia Wachter-Zeh, Jens Zumbrage
2021 2021 IEEE International Symposium on Information Theory (ISIT)  
This paper presents the first decoding algorithm for Gabidulin codes over Galois rings with provable quadratic complexity. 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.
doi:10.1109/isit45174.2021.9517904 fatcat:elshj3pk45ftvmfpw5l3uy6niu