TY  - JOUR
T1  - Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$
AU  - Çalışkan, Basri
PY  - 2020
DA  - December
Y2  - 2020
JF  - Conference Proceedings of Science and Technology
PB  - Murat TOSUN
WT  - DergiPark
SN  - 2651-544X
SP  - 19
EP  - 23
VL  - 3
IS  - 1
LA  - en
AB  - 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.
KW  - Duality
KW  - Generator matrix
KW  - Lee weight
KW  - Linear codes over rings
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UR  - https://dergipark.org.tr/tr/pub/cpost/issue//763109
L1  - https://dergipark.org.tr/tr/download/article-file/1184837
ER  -