A characterization of Z2Z2[u]-linear codes

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Abstract

© 2017, Springer Science+Business Media, LLC. We prove that the class of Z2Z2[ u] -linear codes is exactly the class of Z2-linear codes with automorphism group of even order. Using this characterization, we give examples of known codes, e.g. perfect codes, which have a nontrivial Z2Z2[ u] structure. Moreover, we exhibit some examples of Z2-linear codes which are not Z2Z2[ u] -linear. Also, we state that the duality of Z2Z2[ u] -linear codes is the same as the duality of Z2-linear codes. Finally, we prove that the class of Z2Z4-linear codes which are also Z2-linear is strictly contained in the class of Z2Z2[ u] -linear codes.
Original languageEnglish
Pages (from-to)1377-1389
JournalDesigns, Codes, and Cryptography
Volume86
Issue number7
DOIs
Publication statusPublished - 1 Jul 2018

Keywords

  • Z -linear codes 2
  • Z Z -linear codes 2 4
  • Z Z [ u] -linear codes 2 2

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