A Welch–Berlekamp Like Algorithm for Decoding Gabidulin Codes
In this paper, we present a new approach of the decoding of Gabidulin codes. We show that, in the same way as decoding Reed-Solomon codes is an instance of the problem called polynomial reconstruction, the decoding of Gabidulin codes can be seen as an instance of the problem of reconstruction of linearized polynomials. This approach leads to the design of two efficient decoding algorithms inspired from the Welch–Berlekamp decoding algorithm for Reed–Solomon codes. The first algorithm has the same complexity as the existing ones, that is cubic in the number of errors, whereas the second has quadratic complexity in 2.5n 2 – 1.5k 2.
KeywordsDecode Algorithm Rank Distance Solomon Code Quadratic Complexity Decode Problem
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- 1.Berlekamp, E.R., Welch, L.: Error correction of algebraic block codes. US Patent, Number 4,633,470 (1986)Google Scholar
- 2.Chabaud, F., Stern, J.: The cryptographic security of the syndrome decoding problem for rank distance codes. In: Kim, K.-c., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163. Springer, Heidelberg (1996)Google Scholar
- 10.Richter, G., Plass, S.: Error and erasure decoding of rank-codes with a modified Berlekamp-Massey algorithm. In: 5th Int. ITG Conference on Source and Channel Coding (SCC 2004) (2004)Google Scholar
- 12.Sudan, M.: Decoding Reed-Solomon codes beyond the error-correction diameter. In: Proceedings of the 35th Annual Allerton Conference on Communication, Control and Computing, pp. 215–224 (1997)Google Scholar