Year 2020, Volume 7 , Issue 1, Pages 85 - 101 2020-02-29

$\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})-$ linear skew constacyclic codes

Ahlem MELAKHESSOU [1] , Nuh AYDİN [2] , Zineb HEBBACHE [3] , Kenza GUENDA [4]


In this paper, we study skew constacyclic codes over the ring $\mathbb{Z}_{q}R$ where $R=\mathbb{Z}_{q}+u\mathbb{Z}_{q}$, $q=p^{s}$ for a prime $p$ and $u^{2}=0.$ We give the definition of these codes as subsets of the ring $\mathbb{Z}_{q}^{\alpha}R^{\beta}$. Some structural properties of the skew polynomial ring $ R[x,\Theta]$ are discussed, where $ \Theta$ is an automorphism of $R.$ We describe the generator polynomials of skew constacyclic codes over $\mathbb{Z}_{q}R,$ also we determine their minimal spanning sets and their sizes. Further, by using the Gray images of skew constacyclic codes over $\mathbb{Z}_{q}R$ we obtained some new linear codes over $\mathbb{Z}_{4}$. Finally, we have generalized these codes to double skew constacyclic codes over $\mathbb{Z}_{q}R$.
Linear codes, Skew constacyclic codes, $\mathbb{Z}_{q}\mathbb{Z}_{q}, Bounds
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Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Author: Ahlem MELAKHESSOU
Institution: Mostefa Ben Boulaid University
Country: Algeria


Author: Nuh AYDİN
Institution: Kenyon College
Country: United States


Author: Zineb HEBBACHE
Institution: Faculty of Mathematics, USTHB
Country: Algeria


Author: Kenza GUENDA (Primary Author)
Institution: Faculty of Mathematics, USTHB
Country: Algeria


Dates

Publication Date : February 29, 2020

Bibtex @research article { jacodesmath671815, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2020}, volume = {7}, pages = {85 - 101}, doi = {10.13069/jacodesmath.671815}, title = {\$\\mathbb\{Z\}\_\{q\}(\\mathbb\{Z\}\_\{q\}+u\\mathbb\{Z\}\_\{q\})-\$ linear skew constacyclic codes}, key = {cite}, author = {Melakhessou, Ahlem and Aydi̇n, Nuh and Hebbache, Zineb and Guenda, Kenza} }
APA Melakhessou, A , Aydi̇n, N , Hebbache, Z , Guenda, K . (2020). $\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})-$ linear skew constacyclic codes . Journal of Algebra Combinatorics Discrete Structures and Applications , 7 (1) , 85-101 . DOI: 10.13069/jacodesmath.671815
MLA Melakhessou, A , Aydi̇n, N , Hebbache, Z , Guenda, K . "$\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})-$ linear skew constacyclic codes" . Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 85-101 <https://dergipark.org.tr/en/pub/jacodesmath/issue/51990/671815>
Chicago Melakhessou, A , Aydi̇n, N , Hebbache, Z , Guenda, K . "$\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})-$ linear skew constacyclic codes". Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 85-101
RIS TY - JOUR T1 - $\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})-$ linear skew constacyclic codes AU - Ahlem Melakhessou , Nuh Aydi̇n , Zineb Hebbache , Kenza Guenda Y1 - 2020 PY - 2020 N1 - doi: 10.13069/jacodesmath.671815 DO - 10.13069/jacodesmath.671815 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 85 EP - 101 VL - 7 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.671815 UR - https://doi.org/10.13069/jacodesmath.671815 Y2 - 2019 ER -
EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications $\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})-$ linear skew constacyclic codes %A Ahlem Melakhessou , Nuh Aydi̇n , Zineb Hebbache , Kenza Guenda %T $\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})-$ linear skew constacyclic codes %D 2020 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 7 %N 1 %R doi: 10.13069/jacodesmath.671815 %U 10.13069/jacodesmath.671815
ISNAD Melakhessou, Ahlem , Aydi̇n, Nuh , Hebbache, Zineb , Guenda, Kenza . "$\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})-$ linear skew constacyclic codes". Journal of Algebra Combinatorics Discrete Structures and Applications 7 / 1 (February 2020): 85-101 . https://doi.org/10.13069/jacodesmath.671815
AMA Melakhessou A , Aydi̇n N , Hebbache Z , Guenda K . $\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})-$ linear skew constacyclic codes. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(1): 85-101.
Vancouver Melakhessou A , Aydi̇n N , Hebbache Z , Guenda K . $\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})-$ linear skew constacyclic codes. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(1): 85-101.