On Fast Interpolation Method for Guruswami-Sudan List Decoding of One-Point Algebraic-Geometry Codes
Fast interpolation methods for the original and improved versions of list decoding of one-point algebraic-geometry codes are presented. The methods are based on the Gröbner basis theory and the BMS algorithm for multiple arrays, although their forms are different in the original list decoding algorithm (Sudan algorithm) and the improved list decoding algorithm (Guruswami-Sudan algorithm). The computational complexity is less than that of the conventional Gaussian elimination method.
KeywordsTotal Order Pole Order Multiple Array List Decode Receive Word
Unable to display preview. Download preview PDF.
- 5.Y. Numakami, M. Fujisawa, S. Sakata, “A fast interpolation method for list decoding of Reed-Solomon codes,” Trans. IEICE, J83-A, 1309–1317, 2000. (in Japanese)Google Scholar
- 6.V. Olshevsky, M. A. Shokrollahi, “A displacement approach to efficient decoding of algebraic-geometric codes,” Proc. 31st ACM Symp. Theory of Comput., 235–244, 1999.Google Scholar
- 8.R. Matsumoto, “On the second step in the Guruswami-Sudan list decoding for AG codes,” Tech. Report of IEICE, IT99-75, 65–70, 2000.Google Scholar
- 9.X. W. Wu, P. H. Siegel, “Efficient list decoding of algebraic-geometric codes beyond the error correction bound,” preprint.Google Scholar
- 10.Sh. Gao, M. A. Shokrollahi, “Computing roots of the polynomials over function fields of curves,” in D. Joyner (Ed.), Coding Theory & Crypt., Springer, 214–228, 2000.Google Scholar
- 11.S. Sakata, “N-dimensional Berlekamp-Massey algorithm for multiple arrays and construction of multivariate polynomials with preassigned zeros,” in T. Mora (Ed.), Appl. Algebra, AlgebraicA lgorithms & Error-Correcting Codes, LNCS: 357, Springer, 356–376, 1989.Google Scholar
- 12.S. Sakata, Y. Numakami, “A fast interpolation method for list decoding of RS and algebraic-geometric codes,” presented at the 2000 IEEE Intern. Symp. Inform. Theory, Sorrento, Italy, June 2000.Google Scholar
- 14.R. Nielsen, T. Høholdt, “Decoding Reed-Solomon codes beyond half the minimum distance,” in J. Buchmenn, T. Høholdt, T. Stichtenoth, H. Tapia-Recillas (Eds.), Coding Theory, Crypt. & Related Areas, Springer, 221–236, 2000.Google Scholar
- 15.T. Høholdt, R. Nielsen, “Decoding Hermitian codes with Sudan’s algorithm,” preprint.Google Scholar
- 16.W. Feng, R. E. Blahut, “Some results of the Sudan algorithm” presented at the 1998 IEEE Intern. Symp. Inform. Theory, Cambridge, USA, August 1998.Google Scholar