There is exactly one Z2Z4-cyclic 1-perfect code

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Abstract

© 2016, Springer Science+Business Media New York. Let C be a Z2Z4-additive code of length n> 3. We prove that if the binary Gray image of C is a 1-perfect nonlinear code, then C cannot be a Z2Z4-cyclic code except for one case of length n= 15. Moreover, we give a parity check matrix for this cyclic code. Adding an even parity check coordinate to a Z2Z4-additive 1-perfect code gives a Z2Z4-additive extended 1-perfect code. We also prove that such a code cannot be Z2Z4-cyclic.
Original languageEnglish
Pages (from-to)557-566
JournalDesigns, Codes, and Cryptography
Volume85
Issue number3
DOIs
Publication statusPublished - 1 Dec 2017

Keywords

  • Perfect codes
  • Simplex codes
  • Z Z -additive cyclic codes 2 4

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