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Parameterized codes over graphs

  • Special Issue in Honor of Rafael H. Villarreal on the Occasion of His 70th Birthday
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Abstract

In this article we review known results on parameterized linear codes over graphs, introduced by Rentería et al. (Finite Fields Appl 17(1):81–104, 2011) . Very little is known about their basic parameters and invariants. We review in detail the parameters dimension, regularity and minimum distance. As regards the parameter dimension, we explore the connection to Eulerian ideals in the ternary case and we give new combinatorial formulas.

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Funding

Jorge Neves was partially supported by the Centre for Mathematics of the University of Coimbra - UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES. Maria Vaz Pinto was partially supported by FCT/Portugal through CAMGSD, IST-ID, projects UIDB/04459/2020 and UIDP/04459/2020.

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Authors and Affiliations

  1. Department of Mathematics, CMUC, University of Coimbra, 3001-501, Coimbra, Portugal

    Jorge Neves

  2. Department of Mathematics, IST, University of Lisbon, Avenida Rovisco Pais, 1049-001, Lisbon, Portugal

    Maria Vaz Pinto

Authors
  1. Jorge Neves
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  2. Maria Vaz Pinto
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Correspondence to Maria Vaz Pinto.

Additional information

Communicated by Carlos Rentería.

Dedicated to Rafael Villarreal, on the occasion of his 70th birthday.

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Neves, J., Vaz Pinto, M. Parameterized codes over graphs. São Paulo J. Math. Sci. 17, 306–319 (2023). https://doi.org/10.1007/s40863-022-00335-7

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  • DOI: https://doi.org/10.1007/s40863-022-00335-7

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