关于Justesen代数几何码
ON JUSTESENS ALGEBRAIC GEOMETRY CODES
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摘要: 本文通过建立保持Hamming距离的同构,给出了研究Justesen等(1989)所构造的代数几何码的一般方法,并取得一些新的结果。本文在进行译码研究时,首次把同类型的较小的代数几何码的码字与错误位置多项式的值相对应,从而清晰地揭示了译码过程,以及纠错能力。本文还得到一般代数几何码维数的上界和下界。最后给出了一个容易理解的译码算法。此算法类似于RS码的Peterson译码算法。Abstract: An isomorphism preserving Hamming weight between two algebraic geometry (AG) codes is presented to obtain the main parameters of Justesen s algebraic geometry (JAG) codes. To deduce a simple approach to the decoding algorithm, a code word in a small JAG code is used to correspond to error-locator polynomial. By this means, a simple decoding procedure and the ability of error correcting are explored obviously. The low and up bounds of the dimension of AG codes are also obtained.
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J. Justesen et al., IEEE Trans. on IT-35(1989)4, 811-821.[2]A. N. Skorobogatov, S.G.Vladut, IEEE Trans. on IT, IT-36(1990)5, 1051-1060.[3]S. Iitaka, Algebraic Geometry, New York: Springer-Verlag, (1982), pp. 185-187.[4]R. Blahut, Theory and Practice of Error Control Codes, MA: Addison-Wesley, (1983), pp. I80-200. -
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