Families of twisted tensor product codes

Designs, Codes and Cryptography volume 67, pages375–384(2013)Cite this article

Abstract

Using geometric properties of the variety \({\mathcal V_{r,t}}\) , the image under the Grassmannian map of a Desarguesian (t − 1)-spread of PG(rt − 1, q), we introduce error correcting codes related to the twisted tensor product construction, producing several families of constacyclic codes. We determine the precise parameters of these codes and characterise the words of minimum weight.

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Author information

Affiliations

  1. Department of Mathematics, Facoltà di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, Brescia, 25133, Italy

    Luca Giuzzi

  2. Department of Mathematics, Universiteit Gent, Building S22, Krijgslaan 281, Gent, 9000, Belgium

    Valentina Pepe

Authors
  1. Luca Giuzzi
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  2. Valentina Pepe
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Corresponding author

Correspondence to Valentina Pepe.

Additional information

L. Giuzzi—Part of this research has been performed while a guest of the Department of Mathematics of Ghent University.

Communicated by G. Lunardon.

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Giuzzi, L., Pepe, V. Families of twisted tensor product codes. Des. Codes Cryptogr. 67, 375–384 (2013). https://doi.org/10.1007/s10623-012-9613-6

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Keywords

  • Segre product
  • Veronesean
  • Grassmannian
  • Desarguesian spread
  • Subgeometry
  • Twisted product
  • Constacyclic error correcting code
  • Minimum weight

Mathematics Subject Classification (2010)

  • 94B05
  • 94B27
  • 15A69
  • 51E20