Research Article
BibTex RIS Cite

QUANTUM CODES FROM CODES OVER THE RING $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$

Year 2019, Volume: 2 Issue: 2, 127 - 136, 29.07.2019

Murat Güzeltepe , Mustafa Eröz

https://doi.org/10.33773/jum.590694
Cited By: 1

Abstract

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.

Keywords

quantum codes linear codes

Project Number

116F318

References

  • [1] Calderbank A. R., Rains, E. M., Shor, P. W., Sloane, N. J. A., "Quantum error correction via codes over $GF (4)$", IEEE Trans. Inform. Theory, vol. 44, pp. 1369- 1387, 1998.
  • [2] Kai X., Zhu S., "Quaternary construction of quantum codes from cyclic codes over $\mathbb{F}_4+u\mathbb{F}_4$", Int. Journal of Quantum Inf., vol. 9, no. 2, pp. 689-700, 2011.
  • [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.
  • [4] YoungJu Choie, Steven T. Dougherty, "Codes over $\Sigma _{2m}$ and Jacobi forms over Quaternions", AAECC, vol. 15, pp. 129-147, 2004.
  • [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)
  • [6] Davidoff, G., Sarnak, P., Valette, A., \emph{Elementary number theory, group theory, and Ramanujan graphs}, Cambridge UniversityPress, 2003.

Year 2019, Volume: 2 Issue: 2, 127 - 136, 29.07.2019

Murat Güzeltepe , Mustafa Eröz

https://doi.org/10.33773/jum.590694
Cited By: 1

Abstract

Supporting Institution

TÜBİTAK

Project Number

116F318

References

  • [1] Calderbank A. R., Rains, E. M., Shor, P. W., Sloane, N. J. A., "Quantum error correction via codes over $GF (4)$", IEEE Trans. Inform. Theory, vol. 44, pp. 1369- 1387, 1998.
  • [2] Kai X., Zhu S., "Quaternary construction of quantum codes from cyclic codes over $\mathbb{F}_4+u\mathbb{F}_4$", Int. Journal of Quantum Inf., vol. 9, no. 2, pp. 689-700, 2011.
  • [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.
  • [4] YoungJu Choie, Steven T. Dougherty, "Codes over $\Sigma _{2m}$ and Jacobi forms over Quaternions", AAECC, vol. 15, pp. 129-147, 2004.
  • [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)
  • [6] Davidoff, G., Sarnak, P., Valette, A., \emph{Elementary number theory, group theory, and Ramanujan graphs}, Cambridge UniversityPress, 2003.
There are 6 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Murat Güzeltepe 0000-0002-2089-5660

Mustafa Eröz

Project Number 116F318
Submission Date July 11, 2019
Acceptance Date August 24, 2019
Publication Date July 29, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA Güzeltepe, M., & Eröz, M. (2019). QUANTUM CODES FROM CODES OVER THE RING $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$. Journal of Universal Mathematics, 2(2), 127-136. https://doi.org/10.33773/jum.590694
AMA Güzeltepe M, Eröz M. QUANTUM CODES FROM CODES OVER THE RING $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$. JUM. July 2019;2(2):127-136. doi:10.33773/jum.590694
Chicago Güzeltepe, Murat, and Mustafa Eröz. “QUANTUM CODES FROM CODES OVER THE RING $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$”. Journal of Universal Mathematics 2, no. 2 (July 2019): 127-36. https://doi.org/10.33773/jum.590694.
EndNote Güzeltepe M, Eröz M (July 1, 2019) QUANTUM CODES FROM CODES OVER THE RING $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$. Journal of Universal Mathematics 2 2 127–136.
IEEE M. Güzeltepe and M. Eröz, “QUANTUM CODES FROM CODES OVER THE RING $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$”, JUM, vol. 2, no. 2, pp. 127–136, 2019, doi: 10.33773/jum.590694.
ISNAD Güzeltepe, Murat - Eröz, Mustafa. “QUANTUM CODES FROM CODES OVER THE RING $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$”. Journal of Universal Mathematics 2/2 (July2019), 127-136. https://doi.org/10.33773/jum.590694.
JAMA Güzeltepe M, Eröz M. QUANTUM CODES FROM CODES OVER THE RING $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$. JUM. 2019;2:127–136.
MLA Güzeltepe, Murat and Mustafa Eröz. “QUANTUM CODES FROM CODES OVER THE RING $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$”. Journal of Universal Mathematics, vol. 2, no. 2, 2019, pp. 127-36, doi:10.33773/jum.590694.
Vancouver Güzeltepe M, Eröz M. QUANTUM CODES FROM CODES OVER THE RING $\mathbb{F}_{2^m}+\alpha \mathbb{F}_{2^m}+\beta \mathbb{F}_{2^m}+ \gamma \mathbb{F}_{2^m}$. JUM. 2019;2(2):127-36.

Cited By

Constructions of quasi-twisted quantum codes
Quantum Information Processing
https://doi.org/10.1007/s11128-020-02742-1

33564
https://creativecommons.org/licenses/by-nc-nd/4.0/