Abstract
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.
This work is partly supported by the Science Foundation of the Japanese Educational Ministry under Grant No. 12650368.
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Sakata, S. (2001). On Fast Interpolation Method for Guruswami-Sudan List Decoding of One-Point Algebraic-Geometry Codes. In: Boztaş, S., Shparlinski, I.E. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2001. Lecture Notes in Computer Science, vol 2227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45624-4_18
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DOI: https://doi.org/10.1007/3-540-45624-4_18
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