基于FIA的代數(shù)幾何碼的譯碼
ON THE DECODING OF ALGEBRAIC GEOMETRIC CODES BASED ON FIA
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摘要: 設C是虧格為g的不可約代數(shù)曲線;C*(D,G)為C上的代數(shù)幾何碼,該碼的設計距離為d*=deg(G)-2g+2。本文首先從理論上證明所給算法的合理性,然后給出一種基于基本累次算法(FIA)的譯碼算法。該算法是G.L.Feng等人(1993)提出的算法的改進。它可對[(d*-1)/2]個錯誤的接收向量進行譯碼。運算量與存貯量約為G.L.Feng等人算法的一半,且便于軟硬件實現(xiàn)。
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關(guān)鍵詞:
- 代數(shù)幾何碼; 基本累次算法; 譯碼算法
Abstract: Supposing C is an irreducible algebraic curve of genus g, C*(D, G) is an algebraic geometric code of designed minimum distance d* = degG- 2g+2. This paper, first, proves that the given algorithm is reasonable theoretically, then gives a decoding algorithm based on Fundamental Iterative Algorithm (FIA), which is a modification of the algorithm proposed by G. L. Feng, et al. (1993) and can correct any received code of (d* -1)/2 or less errors with complexity only one half of that of the algorithm proposed by G.L.Feng, et al. The procedure can be implemented easily by hardware or software. -
Justesen J, Larsen K J, Jensen H E, et al. IEEE Trans. on IT, 1989, IT-35(7): 811-821.[2]Skorogatov A N, Vladut S G. IEEE Trans, on IT, 1990, IT-36(9): 1051-1060.[3]Pellikann R. IEEE Trans, on IT, 1989, IT-35(11): 1228-1232.[4]Brigand D L B. Decoding of codes on hyperelliptic curves, LNCS 514, Eurocode90, Proe. International Symposium on Coding Theory and Application. Udine, Italy: Nov. 1990, 126-134.[5]Rotillon D, Thiongly J A. Decoding of codes on the klein quartic, LNCS, Eurocode90, Proc. International Symposium on Coding Theory and Application. Udine, Italy: Nov. 1990, 135-149.[6]Justeaen J, Laraea K J, Jesen H E, et al. IEEE Trans. on IT, 1992, IT-38(1): 111-119.[7]Feng G L, Rao T R N. IEEE Trans. on IT, 1993, IT-39(1): 37-45.[8]Vanlint J H. Algebraic geometric codes, Coding Theory and Design Theory, IMA Volumes in Mathematics and Its Applications, Vol. 20, Springer-Verlag, 1988, 137-162.[9]Fulton W. Algebraic Curves. New York; Benjamin. 1969.[10]Feag G L, Tzeng K K. IEEE Trans. on IT, 1991, IT-37(9):1274-1287. -
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