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http://dx.doi.org/10.14317/jami.2014.083

UNIQUE DECODING OF PLANE AG CODES REVISITED

Lee, Kwankyu (Department of Mathematics and Education, Chosun University)

Publication Information

Journal of applied mathematics & informatics / v.32, no.1_2, 2014 , pp. 83-98 More about this Journal

Abstract

We reformulate an interpolation-based unique decoding algorithm of AG codes, using the theory of Gr $\ddot{o}$ bner bases of modules on the coordinate ring of the base curve. The conceptual description of the reformulated algorithm lets us better understand the majority voting procedure, which is central in the interpolation-based unique decoding. Moreover the smaller Gr $\ddot{o}$ bner bases imply smaller space and time complexity of the algorithm.

Keywords

Algebraic Geometry codes; interpolation decoding; Gr $\ddot{o}$ bner bases;

Citations & Related Records

Reference

1	Gui Liang Feng and T. T. N. Rao, Decoding algebraic-geometric codes up to the designed minimum distance, IEEE Trans. Inf. Theory 39 (1993), no. 1, 37-45. DOI ScienceOn
2	Patrick Fitzpatrick, On the key equation, IEEE Trans. Inf. Theory 41 (1995), no. 5, 1290-1302. DOI ScienceOn
3	Ralf Kotter, A fast parallel implementation of a Berlekamp-Massey algorithm for algebraic-geometric codes, IEEE Trans. Inf. Theory 44 (1998), no. 4, 1353-1368. DOI ScienceOn
4	Kwankyu Lee, Maria Bras-Amoros, and Michael E. O'Sullivan, Unique decoding of plane AG codes via interpolation, IEEE Trans. Inf. Theory 58 (2012), no. 6, 3941-3950. DOI ScienceOn
5	Shinji Miura, Algebraic geometric codes on certain plane curves, Electronics and Communications in Japan 76 (1993), no. 12, 1-13.
6	J. C. Rosales and P. A. Garcia-Sanchez, Numerical semigroups, Developments in Mathematics, vol. 20, Springer, New York, 2009.
7	S. Sakata, J. Justesen, Y. Madelung, H. E. Jensen, and T. Hholdt, A fast decoding method of AG codes from Miura-Kamiya curves $C_ab$ up to half the Feng-Rao bound, Finite Fields and Their Applications 1 (1995), no. 1, 83-101. DOI ScienceOn