Characterization and constructions of self-dual codes over Z2×Z4

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Abstract

Self-dual codes over ℤ 2×ℤ 4 are subgroups of ℤ α2×ℤ β4 that are equal to their orthogonal under an inner-product that relates these codes to the binary Hamming scheme. Three types of self-dual codes are defined. For each type, the possible values α,β such that there exist a self-dual code C⊆ℤ α2×ℤ β4 are established. Moreover, the construction of such a code for each type and possible pair (α,β) is given. The standard techniques of invariant theory are applied to describe the weight enumerators for each type. Finally, we give a construction of self-dual codes from existing self-dual codes. © 2012 AIMS.
Original languageEnglish
Pages (from-to)287-303
JournalAdvances in Mathematics of Communications
Volume6
Issue number3
DOIs
Publication statusPublished - 1 Aug 2012

Keywords

  • Self-dual codes
  • Type I codes
  • Type II codes
  • Z xZ -additive codes 2 4

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