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On Lagrangian–Grassmannian codes

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Abstract

Using the Lagrangian–Grassmannian, a smooth algebraic variety of dimension n(n + 1)/2 that parametrizes isotropic subspaces of dimension n in a symplectic vector space of dimension 2n, we construct a new class of linear codes generated by this variety, the Lagrangian–Grassmannian codes. We explicitly compute their word length, give a formula for their dimension and an upper bound for the minimum distance in terms of the dimension of the Lagrangian–Grassmannian variety.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma Metropolitana-I, 09340, México, D. F., México

    Jesús Carrillo-Pacheco & Felipe Zaldivar

Authors
  1. Jesús Carrillo-Pacheco
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  2. Felipe Zaldivar
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Correspondence to Felipe Zaldivar.

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Communicated by G. Korchmaros.

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Carrillo-Pacheco, J., Zaldivar, F. On Lagrangian–Grassmannian codes. Des. Codes Cryptogr. 60, 291–298 (2011). https://doi.org/10.1007/s10623-010-9434-4

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  • DOI: https://doi.org/10.1007/s10623-010-9434-4

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