4-codes and their Gray map images as orthogonal arrays

Peter Jephson Cameron, Josephine Kusuma, Patrick Solé

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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Abstract

A classic result of Delsarte connects the strength (as orthogonal array) of a linear code with the minimum weight of its dual: the former is one less than the latter.Since the paper of Hammons et al., there is a lot of interest in codes over rings, especially in codes over ℤ4 and their (usually non-linear) binary Gray map images.We show that Delsarte's observation extends to codes over arbitrary finite commutative rings with identity. Also, we show that the strength of the Gray map image of a ℤ4 code is one less than the minimum Lee weight of its Gray map image.
Original languageEnglish
Pages (from-to)109-114
JournalDesigns, Codes and Cryptography
Volume84
Issue number1-2
Early online date20 May 2016
DOIs
Publication statusPublished - Jul 2017

Keywords

  • Commutative ring
  • Code
  • Lee weight
  • Orthogonal array
  • Gray map

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