## Abstract

The {\mathbb{Z}_{{2^s}}}-additive codes are subgroups of \mathbb{Z}_{{2^s}}^n. These codes can be seen as a generalization of linear codes over 2 and 4. A {\mathbb{Z}_{{2^s}}}-linear code is a binary code, not necessarily linear, which is the Gray map image of a {\mathbb{Z}_{{2^s}}}-additive code. In 2014, a systematic encoding was found for 4-linear codes. Moreover, an alternative permutation decoding method, which is suitable for any binary code (not necessarily linear) with a systematic encoding, was established. In this paper, we generalise these results by presenting a systematic encoding for {\mathbb{Z}_{{2^s}}}-linear codes with s > 2. This encoding allows us to perform a permutation decoding for this family of codes.

Original language | English |
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Title of host publication | Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 140-144 |

Number of pages | 5 |

ISBN (Electronic) | 9781665402873 |

DOIs | |

Publication status | Published - 11 Oct 2020 |

### Publication series

Name | Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020 |
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## Keywords

- Gray map
- systematic encoding
- Z-additive codes
- Z-linear codes

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