關(guān)于Justesen代數(shù)幾何碼
ON JUSTESENS ALGEBRAIC GEOMETRY CODES
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摘要: 本文通過建立保持Hamming距離的同構(gòu),給出了研究Justesen等(1989)所構(gòu)造的代數(shù)幾何碼的一般方法,并取得一些新的結(jié)果。本文在進(jìn)行譯碼研究時,首次把同類型的較小的代數(shù)幾何碼的碼字與錯誤位置多項式的值相對應(yīng),從而清晰地揭示了譯碼過程,以及糾錯能力。本文還得到一般代數(shù)幾何碼維數(shù)的上界和下界。最后給出了一個容易理解的譯碼算法。此算法類似于RS碼的Peterson譯碼算法。
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關(guān)鍵詞:
- 代數(shù)幾何碼; 錯誤位置多項式; 伴隨式矩陣; Riemann-Roch定理
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. -
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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