Efficient Decoding of Gabidulin Codes over Galois Rings [article]

Sven Puchinger and Julian Renner and Antonia Wachter-Zeh and Jens Zumbrägel
2021 arXiv   pre-print
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.
arXiv:2102.02157v1 fatcat:ek7z746aojadndtjpkmtgqf5aa