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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

Mustafa Özkan , Figen Öke

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.

Keywords

Lexicographically ordered Hadamard Codes Codes over Ring

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

Mustafa Özkan , Figen Öke

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 Articles
Authors

Mustafa Özkan

Figen Öke

Publication Date April 15, 2018
Submission Date December 19, 2017
Acceptance Date April 6, 2018
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]/ $. Konuralp Journal of Mathematics, 6(1), 54-56.
AMA Özkan M, Öke F. Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/ $. Konuralp J. Math. April 2018;6(1):54-56.
Chicago Özkan, Mustafa, and Figen Öke. “Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/ $”. Konuralp Journal of Mathematics 6, no. 1 (April 2018): 54-56.
EndNote Özkan M, Öke F (April 1, 2018) Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/ $. Konuralp Journal of Mathematics 6 1 54–56.
IEEE M. Özkan and F. Öke, “Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/ $”, Konuralp J. Math., vol. 6, no. 1, pp. 54–56, 2018.
ISNAD Özkan, Mustafa - Öke, Figen. “Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/ $”. Konuralp Journal of Mathematics 6/1 (April 2018), 54-56.
JAMA Özkan M, Öke F. Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/ $. Konuralp J. Math. 2018;6:54–56.
MLA Özkan, Mustafa and Figen Öke. “Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/ $”. Konuralp Journal of Mathematics, vol. 6, no. 1, 2018, pp. 54-56.
Vancouver Özkan M, Öke F. Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/ $. Konuralp J. Math. 2018;6(1):54-6.
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