A novel maximum distance separable code to generate universal identifiers

  • Ismael Gutiérrez García
  • Daladier Jabba Molinares
  • Ivan Molina Naizir


Nowadays it is vital to have a robust mechanism that can identify people, objects, animals, and living beings, for example, for agricultural, health and national security purposes. Some drawbacks occur when very many objects need to be identified, and the tool is unable to support all of them. Even if the mechanism could tag them all, it is also important that the labels or codewords not resemble each other, to be able to detect and correct errors. To solve this problem, this article proposes an MDS (Maximum Distance Separable) code C with length 11 and dimension 7 over the finite field \({\mathbb {F}}_{2^{10}}\). Furthermore, we construct a subcode of C with capacity for 327 different identifiers. Concretely we consider the set of all codewords with entries belonging to the subfield of \({\mathbb {F}}_{2^{10}}\) isomorphic to \({\mathbb {F}}_{2^{5}}\). A decoding algorithm and an encryption method using elliptic curves cryptography for the codewords are also proposed.


Finite fields Binary linear codes MDS-code Maximum distance separable Information theory Elliptic curve cryptosystem Identifiers Error correction Error detection 

Mathematics Subject Classification (2010)

Primary 00-01 Secondary 99-00 



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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Ismael Gutiérrez García
    • 1
  • Daladier Jabba Molinares
    • 2
  • Ivan Molina Naizir
    • 2
  1. 1.Department of Mathematics and StatisticsUniversidad del NorteBarranquillaColombia
  2. 2.Department of Computer ScienceUniversidad del NorteBarranquillaColombia

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