ℤ4-codes and their Gray map images as orthogonal arrays

Peter Jephson Cameron; Josephine Kusuma; Patrick Solé

doi:10.1007/s10623-016-0225-4

ℤ₄-codes and their Gray map images as orthogonal arrays

Peter Jephson Cameron, Josephine Kusuma, Patrick Solé

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	109-114
Journal	Designs, Codes and Cryptography
Volume	84
Issue number	1-2
Early online date	20 May 2016
DOIs	https://doi.org/10.1007/s10623-016-0225-4
Publication status	Published - Jul 2017

Keywords

Commutative ring
Code
Lee weight
Orthogonal array
Gray map

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10.1007/s10623-016-0225-4

OApaper_v7
© 2016, Springer Science+Business Media New York. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at link.springer.com / https://dx.doi.org/10.1007/s10623-016-0225-4
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Cite this

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