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Erschienen in: Designs, Codes and Cryptography 2/2016

01.11.2016

Construction of extremal self-dual codes over \({\mathbb {Z}}_{8}\) and \({\mathbb {Z}}_{16}\)

verfasst von: Boran Kim, Yoonjin Lee

Erschienen in: Designs, Codes and Cryptography | Ausgabe 2/2016

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Abstract

We present a method of constructing free self-dual codes over \({\mathbb {Z}}_8\) and \({\mathbb {Z}}_{16}\) which are extremal or optimal with respect to the Hamming weight. We first prove that every (extremal or optimal) free self-dual code over \({\mathbb {Z}}_{2^m}\) can be found from a binary (extremal or optimal) Type II code for any positive integer \(m \ge 2\). We find explicit algorithms for construction of self-dual codes over \({\mathbb {Z}}_8\) and \({\mathbb {Z}}_{16}\). Our construction method is basically a lifting method. Furthermore, we find an upper bound of minimum Hamming weights of free self-dual codes over \({\mathbb {Z}}_{2^m}\). By using our explicit algorithms, we construct extremal free self-dual codes over \({\mathbb {Z}}_8\) and \({\mathbb {Z}}_{16}\) up to lengths 40.
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Metadaten
Titel
Construction of extremal self-dual codes over and
verfasst von
Boran Kim
Yoonjin Lee
Publikationsdatum
01.11.2016
Verlag
Springer US
Erschienen in
Designs, Codes and Cryptography / Ausgabe 2/2016
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-015-0137-8

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