Z2Z4-linear codes: Generator matrices and duality

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Abstract

A code ℤ2ℤ4-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). In this paper ℤ2ℤ4-additive codes are studied. Their corresponding binary images, via the Gray map, are ℤ2ℤ 4-linear codes, which seem to be a very distinguished class of binary group codes. As for binary and quaternary linear codes, for these codes the fundamental parameters are found and standard forms for generator and parity-check matrices are given. In order to do this, the appropriate concept of duality for ℤ2ℤ4-additive codes is defined and the parameters of their dual codes are computed. © 2009 Springer Science+Business Media, LLC.
Original languageEnglish
Pages (from-to)167-179
JournalDesigns, Codes, and Cryptography
Volume54
Issue number2
DOIs
Publication statusPublished - 1 Feb 2010

Keywords

  • Binary linear codes
  • Duality
  • Quaternary linear codes
  • ℤ ℤ -additive codes 2 4
  • ℤ ℤ -linear codes 2 4

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