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Codes on linear sections of the Grassmannian

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Abstract

We show that for every linear section of a Grassmannian over a finite field \({{\mathbb {F}}}_q\), in addition to the evaluation code associated to the \({{\mathbb {F}}}_q\)-rational points of the section, there exists a parity check code. Instances of these parity check codes are given by linear sections of the Schubert, Lagrangian–Grassmannian, Schubert’s unions, Schubert’s Lagrangian–Grassmannian, and Schubert’s Lagrangian–Grassmannian unions codes

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Acknowledgements

We would like to thank the referees for their comments and suggestions that helped to improve the presentation. J. Carrillo-Pacheco work is supported by the Laboratorio de Cifrado y Codificación de la Información of the Universidad Autónoma de la Ciudad de México.

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Authors and Affiliations

  1. Academia de Matemáticas, Universidad Autónoma de la Ciudad de México, 09790, Ciudad de México, Mexico

    Jesús Carrillo-Pacheco

  2. Departamento de Matemáticas, Universidad Autónoma Metropolitana-I, 09340, Ciudad de México, Mexico

    Felipe Zaldívar

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  1. Jesús Carrillo-Pacheco
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  2. Felipe Zaldívar
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Correspondence to Felipe Zaldívar.

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Carrillo-Pacheco, J., Zaldívar, F. Codes on linear sections of the Grassmannian. Bol. Soc. Mat. Mex. 27, 44 (2021). https://doi.org/10.1007/s40590-021-00351-1

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