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Construction of codes from Arakelov geometry

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Abstract

We give a construction of the codes from Hermitian vector bundles on an arithmetic curve generalizing the number field codes introduced by Guruswami and Lenstra. Using Arakelov geometry, we give an estimate of the parameters of these codes.

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Acknowledgments

The author was supported in part by Grant-in-Aid for Scientific Research (C)(24540052).

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Authors and Affiliations

  1. Department of Mathematical and Physical Sciences, Faculty of Science, Japan Women’s University, Mejirodai, Bunkyoku, Tokyo, 112-8681, Japan

    Tohru Nakashima

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  1. Tohru Nakashima
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Correspondence to Tohru Nakashima.

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Communicated by G. Korchmaros.

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Nakashima, T. Construction of codes from Arakelov geometry. Des. Codes Cryptogr. 73, 47–54 (2014). https://doi.org/10.1007/s10623-013-9809-4

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  • DOI: https://doi.org/10.1007/s10623-013-9809-4

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