@inbook{d9bc0c1ed6db4d79b7ed8d745adc8c14,

title = "Systematic encoding for Z2s-linear codes",

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. ",

keywords = "Gray map, systematic encoding, Z-additive codes, Z-linear codes",

author = "Adrian Torres-Martin and Merce Villanueva",

note = "Publisher Copyright: {\textcopyright} 2020 IEEE.",

year = "2020",

month = oct,

day = "11",

doi = "10.1109/ACCT51235.2020.9383384",

language = "English",

series = "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",

booktitle = "Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020",

}