An evaluation of erasure decoding algorithms for Gabidulin codes

Gabidulin codes are linear block codes over an extension field that can be seen as the analogs of Reed-Solomon codes for the rank metric. Important applications of Gabidulin codes include the areas of network coding and distributed storage, particularly for the problem of rank erasure correction. This paper studies the complexity of erasure decoding algorithms for Gabidulin codes with short-to-moderate (not asymptotically long) block lengths. The two fastest known algorithms are compared in detail (in terms of exact number of operations) and it is shown for which parameter values one algorithm is superior to the other.