6 research outputs found
Efficient Decoding of Gabidulin Codes over Galois Rings
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