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Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/<u^3> $

Year 2018, Volume: 6 Issue: 1, 54 - 56, 15.04.2018
https://izlik.org/JA37BP53RA

Abstract

In this study, the results obtained by authors M. Ozkan and F. Oke [2] is extended the ring $ \mathbb{F}_2[u]/<u^3> $. Certain matrices lexicographically ordered are written using the elements of $ \mathbb{F}_2[u]/<u^3> $. The relations between the codes generated by these matrices and Hadamard codes are given.

References

  • [1] Özkan, M. and Öke, F., On Codes written by matrices Lexicographically ordered, AIP Conf. Proceeding Vol:1926 (2018), 020035-1-020035-3.
  • [2] Özkan, M. and Öke, F., A relation between Hadamard codes and some special codes over F2 +uF2, App Mathematics and Inf. Sci. Vol:10, No:2 (2016), 701-704.
  • [3] Krotov, D. S., Z4-linear perfect codes, Diskretn. Anal. Issled. Oper. Ser.1 Vol:7, No:4 (2000), 78-90.
  • [4] Qian, J. , Zhang, L. and Zhu S., Constacyclic and cycliccodes over F2 +uF2 +u2F2, IEICE Trans. Fundamentals, E89-A, No: 6, (2006)1863-1865.
  • [5] Vermani, L. R., Elements of Algebraic Coding Theorytivity, Chapman Hall , India, 1996.
  • [6] Udomkavanich, P., Jitman, S., On the Gray Image of of ($1 - {u^m}$ )-Cyclic Codes ${\mathbb{F}_{p{\,^k}}}\, + \,u\,{\mathbb{F}_{p{\,^k}}} + ... + {u^m}{\mathbb{F}_{p{\,^k}}}$, Int. J. Contemp. Math. Sciences, Vol.26, No: 4, (2009)1265-1272.

Year 2018, Volume: 6 Issue: 1, 54 - 56, 15.04.2018
https://izlik.org/JA37BP53RA

Abstract

References

  • [1] Özkan, M. and Öke, F., On Codes written by matrices Lexicographically ordered, AIP Conf. Proceeding Vol:1926 (2018), 020035-1-020035-3.
  • [2] Özkan, M. and Öke, F., A relation between Hadamard codes and some special codes over F2 +uF2, App Mathematics and Inf. Sci. Vol:10, No:2 (2016), 701-704.
  • [3] Krotov, D. S., Z4-linear perfect codes, Diskretn. Anal. Issled. Oper. Ser.1 Vol:7, No:4 (2000), 78-90.
  • [4] Qian, J. , Zhang, L. and Zhu S., Constacyclic and cycliccodes over F2 +uF2 +u2F2, IEICE Trans. Fundamentals, E89-A, No: 6, (2006)1863-1865.
  • [5] Vermani, L. R., Elements of Algebraic Coding Theorytivity, Chapman Hall , India, 1996.
  • [6] Udomkavanich, P., Jitman, S., On the Gray Image of of ($1 - {u^m}$ )-Cyclic Codes ${\mathbb{F}_{p{\,^k}}}\, + \,u\,{\mathbb{F}_{p{\,^k}}} + ... + {u^m}{\mathbb{F}_{p{\,^k}}}$, Int. J. Contemp. Math. Sciences, Vol.26, No: 4, (2009)1265-1272.
There are 6 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Conference Paper
Authors

Mustafa Özkan

Figen Öke

Submission Date December 19, 2017
Acceptance Date April 6, 2018
Publication Date April 15, 2018
IZ https://izlik.org/JA37BP53RA
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Özkan, M., & Öke, F. (2018). Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/<u^3> $. Konuralp Journal of Mathematics, 6(1), 54-56. https://izlik.org/JA37BP53RA
AMA 1.Özkan M, Öke F. Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/<u^3> $. Konuralp J. Math. 2018;6(1):54-56. https://izlik.org/JA37BP53RA
Chicago Özkan, Mustafa, and Figen Öke. 2018. “Codes Generated by Special Matrices on $ \mathbb{F}_2[u] <U^3> $”. Konuralp Journal of Mathematics 6 (1): 54-56. https://izlik.org/JA37BP53RA.
EndNote Özkan M, Öke F (April 1, 2018) Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/<u^3> $. Konuralp Journal of Mathematics 6 1 54–56.
IEEE [1]M. Özkan and F. Öke, “Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/<u^3> $”, Konuralp J. Math., vol. 6, no. 1, pp. 54–56, Apr. 2018, [Online]. Available: https://izlik.org/JA37BP53RA
ISNAD Özkan, Mustafa - Öke, Figen. “Codes Generated by Special Matrices on $ \mathbb{F}_2[u] <U^3> $”. Konuralp Journal of Mathematics 6/1 (April 1, 2018): 54-56. https://izlik.org/JA37BP53RA.
JAMA 1.Özkan M, Öke F. Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/<u^3> $. Konuralp J. Math. 2018;6:54–56.
MLA Özkan, Mustafa, and Figen Öke. “Codes Generated by Special Matrices on $ \mathbb{F}_2[u] <U^3> $”. Konuralp Journal of Mathematics, vol. 6, no. 1, Apr. 2018, pp. 54-56, https://izlik.org/JA37BP53RA.
Vancouver 1.Mustafa Özkan, Figen Öke. Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/<u^3> $. Konuralp J. Math. [Internet]. 2018 Apr. 1;6(1):54-6. Available from: https://izlik.org/JA37BP53RA
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