Abstract
An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as \({\mathbb {Z}}_2{\mathbb {Z}}_4\)-linear codes, which are binary and, in general, nonlinear codes in the usual sense. For this, it is proved that these codes allow a systematic encoding scheme. As particular examples, this permutation decoding method is applied to some Hadamard \({\mathbb {Z}}_2{\mathbb {Z}}_4\)-linear codes.
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Acknowledgments
The authors thank Prof. J. Rifà for valuable discussions in an earlier version of this paper. They also thank the anonymous referees for their valuable comments, which enabled them to improve the quality of the paper. This work was partially supported by the Spanish MICINN under Grants TIN2010-17358 and TIN2013-40524-P, and by the Catalan AGAUR under Grant 2009SGR1224. The authors are in alphabetical order.
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Communicated by J. D. Key.
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Bernal, J.J., Borges, J., Fernández-Córdoba, C. et al. Permutation decoding of \({\mathbb {Z}}_2{\mathbb {Z}}_4\)-linear codes. Des. Codes Cryptogr. 76, 269–277 (2015). https://doi.org/10.1007/s10623-014-9946-4
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DOI: https://doi.org/10.1007/s10623-014-9946-4