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Designs, Codes and Cryptography

Erschienen in:

19.07.2017

On some constacyclic codes over \(\mathbb {Z}_{4}\left[ u\right] /\left\langle u^{2}-1\right\rangle \), their \(\mathbb {Z}_4\) images, and new codes

verfasst von: Nuh Aydin, Yasemin Cengellenmis, Abdullah Dertli

Erschienen in: Designs, Codes and Cryptography | Ausgabe 6/2018

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Abstract

In this paper, we study \(\lambda \)-constacyclic codes over the ring \(R=\mathbb {Z}_4+u\mathbb {Z}_4\) where \(u^{2}=1\), for \(\lambda =3+2u\) and \(2+3u\). Two new Gray maps from R to \(\mathbb {Z}_4^{3}\) are defined with the goal of obtaining new linear codes over \(\mathbb {Z}_4\). The Gray images of \(\lambda \)-constacyclic codes over R are determined. We then conducted a computer search and obtained many \(\lambda \)-constacyclic codes over R whose \(\mathbb {Z}_4\)-images have better parameters than currently best-known linear codes over \(\mathbb {Z}_4\).

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Titel: On some constacyclic codes over , their images, and new codes
verfasst von: Nuh Aydin
Yasemin Cengellenmis
Abdullah Dertli
Publikationsdatum: 19.07.2017
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 6/2018
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0392-y

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