On some constacyclic codes over $$\mathbb {Z}_{4}\left[ u\right] /\left\langle u^{2}-1\right\rangle $$, their $$\mathbb {Z}_4$$Z4 images,and new codes |
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Authors: | Nuh Aydin Yasemin Cengellenmis Abdullah Dertli |
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Institution: | 1.Department of Mathematics and Statistics,Kenyon College,Gambier,USA;2.Mathematics Department, Faculty of Arts and Sciences,Trakya University,Edirne,Turkey;3.Mathematics Department, Faculty of Arts and Sciences,Ondokuz Mayis University,Samsun,Turkey |
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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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