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Designs, Codes and Cryptography

, Volume 69, Issue 2, pp 161–180 | Cite as

Additive semisimple multivariable codes over \({\mathbb{F}_4}\)

  • E. Martínez-Moro
  • A. Piñera-Nicolás
  • I. F. Rúa
Article

Abstract

The structure of additive multivariable codes over \({\mathbb{F}_4}\) (the Galois field with 4 elements) is presented. The semisimple case (i.e., when the defining polynomials of the code have no repeated roots) is specifically addressed. These codes extend in a natural way the abelian codes, of which additive cyclic codes of odd length are a particular case. Duality of these codes is also studied.

Keywords

Additive multivariable codes Abelian codes Quantum codes Duality 

Mathematics Subject Classification (2000)

11T61 94B99 81P70 13M10 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • E. Martínez-Moro
    • 1
  • A. Piñera-Nicolás
    • 1
  • I. F. Rúa
    • 2
  1. 1.Institute of Mathematics (IMUVa) and Applied Mathematics DepartmentUniversidad de ValladolidValladolidSpain
  2. 2.Departamento de MatemáticasUniversidad de OviedoOviedoSpain

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