Abstract
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.
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Lee, K. (2014). Magma Implementation of Decoding Algorithms for General Algebraic Geometry Codes. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_21
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DOI: https://doi.org/10.1007/978-3-662-44199-2_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44198-5
Online ISBN: 978-3-662-44199-2
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