Magma Implementation of Decoding Algorithms for General Algebraic Geometry Codes

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• 作者：Kwankyu Lee (17)
  
• 关键词：Decoding algorithm ; Algebraic Geometry coodes ; Algebraic curves
• 刊名：Lecture Notes in Computer Science
• 出版年：2014
• 出版时间：2014
• 年：2014
• 卷：8592
• 期：1
• 页码：119-123
• 全文大小：129 KB
• 参考文献：1. Beelen, P., H?holdt, T.: The decoding of algebraic geometry codes. In: Advances in Algebraic Geometry Codes. Ser. Coding Theory Cryptol., vol.?5, pp. 49-8. World Sci. Publ., Hackensack (2008) CrossRef
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  6. Sakata, S., Jensen, H.E., H?holdt, T.: Generalized Berlekamp-Massey decoding of algebraic-geometric codes up to half the Feng-Rao bound. IEEE Trans. Inf. Theory?41(6), 1762-768 (1995) CrossRef
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  9. Stichtenoth, H.: Algebraic Function Fields and Codes, 2nd edn. Springer (2009)
  
• 作者单位：Kwankyu Lee (17)
  
  17. Department of Mathematics and Education, Chosun University, Korea
  
• ISSN：1611-3349

文摘

Goppa’s codes on algebraic curves defined over finite fields, called AG codes, are usually regarded as the most successful class of error correcting codes in theory as well as in practice. Despite the splendid history of theoretic achievements though, an efficient algorithm decoding general AG codes appeared only recently. The decoding algorithm requires some precomputed data about the Riemann-Roch spaces of functions or differentials of the given curve of positive genus. As Magma is particularly good at computing with these spaces, the algorithm was implemented on Magma. We present its Magma implementation and describe certain details of the implementation.