Conference Paper

Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$

Volume: 3 Number: 1 December 15, 2020
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Conference Proceedings of Science and Technology
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Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$

Abstract

In this paper, we introduce the ring $R=\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$ where $u^{2}=u$, $v^{2}=v$, $uv=vu=0$ over which the linear codes are studied. it's shown that the ring $R=\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$ is a commutative, characteristic 8 ring with $u^{2}=u$, $v^{2}=v$, $uv=vu=0$. Also, the ideals of $\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$ are found. Moreover, we define the Lee distance and the Lee weight of an element of $R$ and investigate the generator matrices of the linear code and its dual.

Keywords

References

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  2. 2 S.T.Dougherty, P. Gaborit, M. Harada, P.Solé, Type II codes over F2 + uF2, IEEE Trans. Inf. Theory 45 (1999), 32–45.
  3. 3 B. Yildiz and S. Karadeniz, Linear Codes over Z4 + uZ4: MacWilliams Identities Projections, and Formally Self-Dual Codes, Finite Fields and Their Applications, 27 (2014), 24–40.
  4. 4 V. Sison and M. Remillion, Isometries and binary images of linear block codes over Z4 + uZ4 and Z8 + uZ8, The Asian Mathematical Conference (AMC 2016), (2016), 313-318.
  5. 5 A. Dertli and Y. Cengellenmis, On the Codes Over the Ring Z4 + uZ4 + vZ4 Cyclic, Constacyclic, Quasi-Cyclic Codes, Their Skew Codes, Cyclic DNA and Skew Cyclic DNA Codes, Prespacetime Journal, 10(2) (2019), 196-213.
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  7. 7 P. Li, X. Guo, S. Zhu, Some results of linear codes over the ring Z4 + uZ4 + vZ4 + uvZ4, Journal of Applied Mathematics and Computing, 54 (2017), 307–324.
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Details

Primary Language

English

Subjects

Engineering

Journal Section

Conference Paper

Authors

Publication Date

December 15, 2020

Submission Date

July 2, 2020

Acceptance Date

September 26, 2020

Published in Issue

Year 2020 Volume: 3 Number: 1

IZ

https://izlik.org/JA69XL87NF

Cite

RIS / Bibtex
APA
Çalışkan, B. (2020). Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$. Conference Proceedings of Science and Technology, 3(1), 19-23. https://izlik.org/JA69XL87NF
AMA
1.Çalışkan B. Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$. Conference Proceedings of Science and Technology. 2020;3(1):19-23. https://izlik.org/JA69XL87NF
Chicago
Çalışkan, Basri. 2020. “Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$”. Conference Proceedings of Science and Technology 3 (1): 19-23. https://izlik.org/JA69XL87NF.
EndNote
Çalışkan B (December 1, 2020) Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$. Conference Proceedings of Science and Technology 3 1 19–23.
IEEE
[1]B. Çalışkan, “Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$”, Conference Proceedings of Science and Technology, vol. 3, no. 1, pp. 19–23, Dec. 2020, [Online]. Available: https://izlik.org/JA69XL87NF
ISNAD
Çalışkan, Basri. “Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$”. Conference Proceedings of Science and Technology 3/1 (December 1, 2020): 19-23. https://izlik.org/JA69XL87NF.
JAMA
1.Çalışkan B. Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$. Conference Proceedings of Science and Technology. 2020;3:19–23.
MLA
Çalışkan, Basri. “Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$”. Conference Proceedings of Science and Technology, vol. 3, no. 1, Dec. 2020, pp. 19-23, https://izlik.org/JA69XL87NF.
Vancouver
1.Basri Çalışkan. Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$. Conference Proceedings of Science and Technology [Internet]. 2020 Dec. 1;3(1):19-23. Available from: https://izlik.org/JA69XL87NF