SeMA Journal

, Volume 73, Issue 1, pp 85–95 | Cite as

Recovering erasures by using MDS codes over extension alphabets

  • Sara D. Cardell
  • Joan-Josep ClimentEmail author


A new family of \({\mathbb {F}}_{q}\)-linear codes over \({\mathbb {F}}_{q}^{b}\) can be obtained replacing the elements in the large field \({\mathbb {F}}_{q^{b}}\) by elements in \({\mathbb {F}}_{q}[C]\), where C is the companion matrix of a primitive polynomial of degree b and coefficients in \({\mathbb {F}}_{q}\). In this work, we propose a decoding algorithm for this family of \({\mathbb {F}}_{q}\)-linear codes over the erasure channel, based on solving linear systems over the field \({\mathbb {F}}_{q}\).


\({\mathbb {F}}_{q}\)-linear code Companion matrix Primitive polynomial Superregular matrix Erasure channel Linear system 

Mathematics Subject Classification

94B35 94B60 



The work of the first author was partially supported by a grant for postdoctoral students from FAPESP with reference 2015/07246-0.


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Copyright information

© Sociedad Española de Matemática Aplicada 2015

Authors and Affiliations

  1. 1.Instituto de Matemática, Estatística e Computação CientíficaUniversidade Estadual de Campinas (UNICAMP)CampinasBrazil
  2. 2.Departament de MatemàtiquesUniversitat d’AlacantAlacantSpain

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