TY  - JOUR
T1  - QUANTUM CODES FROM CODES OVER THE RING $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$
AU  - Güzeltepe, Murat
AU  - Eröz, Mustafa
PY  - 2019
DA  - July
Y2  - 2019
DO  - 10.33773/jum.590694
JF  - Journal of Universal Mathematics
JO  - JUM
PB  - Gökhan ÇUVALCIOĞLU
WT  - DergiPark
SN  - 2618-5660
SP  - 127
EP  - 136
VL  - 2
IS  - 2
LA  - en
AB  - Let $i,j,k$ be elements of real quaternions $\mathbb{H}$. Let $\alpha , \beta , \gamma$ be the elements corresponding to $1+i, 1+j, 1+k,$ respectively. In this study, quantum codes from classical codes over $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$ are obtained.
KW  - quantum codes
KW  - linear codes
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CR  - [3] Qian J., "Quantum Codes from Cyclic Codes over $\mathbb{F}_2+v\mathbb{F}_2$", Journal of Information and Computational Science, vol. 10, no. 6, pp. 1715-1722, 2013.
CR  - [4] YoungJu Choie, Steven T. Dougherty, "Codes over $\Sigma _{2m}$ and Jacobi forms over Quaternions", AAECC, vol. 15, pp. 129-147, 2004.
CR  - [5] Yildiz B., Karadeniz S., "Cyclic codes over $\mathbb{F}_{2} + u\mathbb{F}_{2}+v \mathbb{F}_{2}+uv \mathbb{F}_{2}$", Des. Codes Cryptogr., vol. 58, pp. 221–234, 2011. (DOI: 10.1007/s10623-010-9399-3)
CR  - [6] Davidoff, G., Sarnak, P., Valette, A., \emph{Elementary number theory, group theory, and Ramanujan graphs}, Cambridge UniversityPress, 2003.
UR  - https://doi.org/10.33773/jum.590694
L1  - https://dergipark.org.tr/tr/download/article-file/876172
ER  -