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Lifting iso-dual algebraic geometry codes

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Abstract

In this work we investigate the problem of producing iso-dual algebraic geometry (AG) codes over a finite field \(\mathbb {F}_{q}\) with q elements. Given a finite separable extension \(\mathcal {M}/\mathcal {F}\) of function fields and an iso-dual AG-code \(\mathcal {C}\) defined over \(\mathcal {F}\), we provide a general method to lift the code \(\mathcal {C}\) to another iso-dual AG-code \(\tilde{\mathcal {C}}\) defined over \(\mathcal {M}\) under some assumptions on the parity of the involved different exponents. We apply this method to lift iso-dual AG-codes over the rational function field to elementary abelian p-extensions, like the maximal function fields defined by the Hermitian, Suzuki, and one covered by the GGS function field. We also obtain long binary and ternary iso-dual AG-codes defined over cyclotomic extensions.

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Funding

The first, second and fourth authors are partially supported by CONICET, FONCyT, SECyT-UNC, and CAI+D-UNL. The third author was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, CAPES MATH AMSUD 88881.647739/2021-01.

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Authors and Affiliations

  1. CONICET, Facultad de Ingeniería Química, Universidad Nacional del Litoral, Santiago del Estero 2829, 3000, Santa Fe, Argentina

    María Chara

  2. FaMAF - CIEM (CONICET), Universidad Nacional de Córdoba, Av. Medina Allende 2144, Ciudad Universitaria, 5000, Cordoba, Argentina

    Ricardo Podestá

  3. Centro de Tecnologia, Universidade Federal do Rio de Janeiro, Cidade Universitária, Av. Athos da Silveira Ramos 149, Ilha do Fundão, Rio de Janeiro, CEP 21.941-909, Brazil

    Luciane Quoos

  4. Facultad de Ingeniería Química, Universidad Nacional del Litoral, Santiago del Estero 2829, 3000, Santa Fe, Argentina

    Ricardo Toledano

Authors
  1. María Chara
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  2. Ricardo Podestá
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  3. Luciane Quoos
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  4. Ricardo Toledano
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All authors have contributed equally.

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Correspondence to María Chara.

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All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

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Communicated by G. Korchmaros.

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Chara, M., Podestá, R., Quoos, L. et al. Lifting iso-dual algebraic geometry codes. Des. Codes Cryptogr. (2024). https://doi.org/10.1007/s10623-024-01412-y

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