Research Article
BibTex RIS Cite
Year 2017, Volume: 5 Issue: 1, 93 - 98, 30.04.2017
https://doi.org/10.36753/mathenot.421710

Abstract

References

  • [1] Özkan, M. and Öke F., A relation between Hadamard codes and some special codes over F2 + uF2. App. Mathematics and Inf. Sci 10 (2016), no. 2, 701-704.
  • [2] Jian-Fa,Q.,Zhang L.N. and Zhu S.X.,(1 + u)- cyclic and cyclic codes over the ring F2 + uF2. Applied Mathematics Letters,19, (2006), 820-823.
  • [3] Zhu, S., Wang, Y. and Shi, M., Some result on cyclic codes over F2 + vF2 . IEEE Trans. Inf. Theory, 56, (2010), no.4, 1680-1684.
  • [4] Krotov, D. S., Z4-linear perfect codes. Diskretn. Anal. Issled. Oper,7, (2000),no.4, 78-90.
  • [5] Krotov,D. S., Z4-linear Hadamard and extended perfect codes. Procs. of the International Workshop on Coding and Cryptography,Paris, (2001), 329-334.
  • [6] Vermani, L.,R., Elemants,of Algebraic Coding Theory. Chapman Hall, India, (1996).
  • [7] Wolfmann J., Negacyclic and cyclic codes over Z4. IEEE Trans. Inf. Theory, 45, (1999), 2527-2532.
  • [8] Bonnecaze A. and Udaya P., Cyclic codes and self dual codes F2 + uF2. IEEE Trans. Inf. Theory, 45, (1999), 1250-1255.
  • [9] Özkan, M. and Öke F., On Some Special Codes Over F3 + vF3 + uF3 + u2F3. Mathematical Sci. and App. E-Notes 4 (2016), no.1, 40-44.
  • [10] Özkan, M. and Öke F., Gray images of (1 + v)− constacyclic codes over a particular ring. Palestine Journal of Mathematics, (accepted).

Codes Defined via Especial Matrices over the Ring and Hadamard Codes

Year 2017, Volume: 5 Issue: 1, 93 - 98, 30.04.2017
https://doi.org/10.36753/mathenot.421710

Abstract

In this study, certain matrices are obtained using the elements of a finite chain ring. Then using these
matrices as generator matrices; certain codes and their duals are obtained. Moreover relations between
these codes, binary codes and Hadamard codes are explained.

References

  • [1] Özkan, M. and Öke F., A relation between Hadamard codes and some special codes over F2 + uF2. App. Mathematics and Inf. Sci 10 (2016), no. 2, 701-704.
  • [2] Jian-Fa,Q.,Zhang L.N. and Zhu S.X.,(1 + u)- cyclic and cyclic codes over the ring F2 + uF2. Applied Mathematics Letters,19, (2006), 820-823.
  • [3] Zhu, S., Wang, Y. and Shi, M., Some result on cyclic codes over F2 + vF2 . IEEE Trans. Inf. Theory, 56, (2010), no.4, 1680-1684.
  • [4] Krotov, D. S., Z4-linear perfect codes. Diskretn. Anal. Issled. Oper,7, (2000),no.4, 78-90.
  • [5] Krotov,D. S., Z4-linear Hadamard and extended perfect codes. Procs. of the International Workshop on Coding and Cryptography,Paris, (2001), 329-334.
  • [6] Vermani, L.,R., Elemants,of Algebraic Coding Theory. Chapman Hall, India, (1996).
  • [7] Wolfmann J., Negacyclic and cyclic codes over Z4. IEEE Trans. Inf. Theory, 45, (1999), 2527-2532.
  • [8] Bonnecaze A. and Udaya P., Cyclic codes and self dual codes F2 + uF2. IEEE Trans. Inf. Theory, 45, (1999), 1250-1255.
  • [9] Özkan, M. and Öke F., On Some Special Codes Over F3 + vF3 + uF3 + u2F3. Mathematical Sci. and App. E-Notes 4 (2016), no.1, 40-44.
  • [10] Özkan, M. and Öke F., Gray images of (1 + v)− constacyclic codes over a particular ring. Palestine Journal of Mathematics, (accepted).
There are 10 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Mustafa Özkan

Figen Öke

Publication Date April 30, 2017
Submission Date December 31, 2016
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Özkan, M., & Öke, F. (2017). Codes Defined via Especial Matrices over the Ring and Hadamard Codes. Mathematical Sciences and Applications E-Notes, 5(1), 93-98. https://doi.org/10.36753/mathenot.421710
AMA Özkan M, Öke F. Codes Defined via Especial Matrices over the Ring and Hadamard Codes. Math. Sci. Appl. E-Notes. April 2017;5(1):93-98. doi:10.36753/mathenot.421710
Chicago Özkan, Mustafa, and Figen Öke. “Codes Defined via Especial Matrices over the Ring and Hadamard Codes”. Mathematical Sciences and Applications E-Notes 5, no. 1 (April 2017): 93-98. https://doi.org/10.36753/mathenot.421710.
EndNote Özkan M, Öke F (April 1, 2017) Codes Defined via Especial Matrices over the Ring and Hadamard Codes. Mathematical Sciences and Applications E-Notes 5 1 93–98.
IEEE M. Özkan and F. Öke, “Codes Defined via Especial Matrices over the Ring and Hadamard Codes”, Math. Sci. Appl. E-Notes, vol. 5, no. 1, pp. 93–98, 2017, doi: 10.36753/mathenot.421710.
ISNAD Özkan, Mustafa - Öke, Figen. “Codes Defined via Especial Matrices over the Ring and Hadamard Codes”. Mathematical Sciences and Applications E-Notes 5/1 (April 2017), 93-98. https://doi.org/10.36753/mathenot.421710.
JAMA Özkan M, Öke F. Codes Defined via Especial Matrices over the Ring and Hadamard Codes. Math. Sci. Appl. E-Notes. 2017;5:93–98.
MLA Özkan, Mustafa and Figen Öke. “Codes Defined via Especial Matrices over the Ring and Hadamard Codes”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 1, 2017, pp. 93-98, doi:10.36753/mathenot.421710.
Vancouver Özkan M, Öke F. Codes Defined via Especial Matrices over the Ring and Hadamard Codes. Math. Sci. Appl. E-Notes. 2017;5(1):93-8.

20477

The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.