2017
DOI: 10.3906/mat-1602-35
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Cyclic codes over $\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}$

Abstract: In this paper, we study cyclic codes over the ring R = Z4 + uZ4 + u 2 Z4 , where u 3 = 0 . We investigate Galois extensions of this ring and the ideal structure of these extensions. The results are then used to obtain facts about cyclic codes over R . We also determine the general form of the generator of a cyclic code and find its minimal spanning sets. Finally, we obtain many new linear codes over Z4 by considering Gray images of cyclic codes over R .

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Cited by 4 publications
(5 citation statements)
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References 6 publications
(7 reference statements)
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“…Ozen et al in [15] have determined cyclic codes over the ring R = Z 4 + uZ 4 + u 2 Z 4 , where u 3 = 0. They obtained that the total number of cyclic codes over R is 13 r .…”
Section: Preliminariesmentioning
confidence: 99%
See 3 more Smart Citations
“…Ozen et al in [15] have determined cyclic codes over the ring R = Z 4 + uZ 4 + u 2 Z 4 , where u 3 = 0. They obtained that the total number of cyclic codes over R is 13 r .…”
Section: Preliminariesmentioning
confidence: 99%
“…Similarly, we get p 3 (x) = q 3 (x). Now, we study the reverse constraint of one generator cyclic code of odd length n over R. For this, first we need the following result which states one generator cyclic codes of odd length n over the ring R. This result with its proof can be found in [15].…”
Section: Cyclic Dna Codes Over Rmentioning
confidence: 99%
See 2 more Smart Citations
“…Kumar et al [16] concentrated the DNA construction and binary images of DNA codes over the ring Z 4 +vZ 4 when v 2 = v . Besides all these studies, if we talked about the various rings with 64 elements; Özen et al [19] investigated the structure of the ring Z 4 + uZ 4 + u 2 Z 4 where u 3 = 0 and Galois extensions of this ring. They also studied the ideal structure of these extensions and used their results to obtain for the cyclic codes over this ring.…”
Section: Introductionmentioning
confidence: 99%