MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING

Volume: 6 Number: 1 July 23, 2016
  • Mehmet Özen
  • Fatma Zehra Uzekmek
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MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING

Abstract

Linear codes are considered over the ring [ ]. The Lee weight enumerators, the complete weight enumerators and the symmetrized weight enumerators for the linear codes over the ring [ ] are defined and Gray map [ ] from [ ] is constructed. Then MacWilliams identities for these weight enumerators are proved.

Keywords

References

  1. S.T. Dougherty, P. Gaborit, M. Harada & P. Sole (1999). Type II Codes over F2 uF2 Theory, 45, 32-45.
  2. B. Yildiz & S. Karadeniz (2014). Linear Codes over ] u]: Macwilliams Identities, Projections and Formally
  3. Self-Dual Codes, Finite Fields Appl., 27, 24-40. Yu H. & Zhu S. (2006). Identities of linear codes and their Codes over F2 uF2 and Technology of Chain, 36 (12): 1285-1288.
  4. R.K. Bandi &M. Baintwal, Codes over ] , IEEE. u], IEEE. B. Yildiz & S. Karadeniz (2010). Linear Codes over F2 uF2 vF2 uvF2
  5. J. Gao (2015). Some Results on Linear Codes over F p uFp u Fp, J. Appl. Math. Comput., 47:473-485.
  6. A.R. Hammons, P.V/ Kumar, A.R. Calderbank, N.J.A. Sloane & P. Sole (1994). The ]
  7. Linearity of Kerdock, Preparata, Goethals and Related Codes, IEEE Transactions on Information Theory, Vol. 40, No.2, pp. 301-319.

Details

Primary Language

English

Subjects

-

Journal Section

-

Authors

Mehmet Özen This is me
Department of Mathematics, Sakarya University, Turkey

Fatma Zehra Uzekmek This is me
Department of Mathematics, Sakarya University, Turkey

Publication Date

July 23, 2016

Submission Date

July 23, 2016

Acceptance Date

-

Published in Issue

Year 2016 Volume: 6 Number: 1

IZ

https://izlik.org/JA73TC67GC

Cite

RIS / Bibtex
APA
Özen, M., & Uzekmek, F. Z. (2016). MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING. TOJSAT, 6(1), 40-44. https://izlik.org/JA73TC67GC
AMA
1.Özen M, Uzekmek FZ. MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING. TOJSAT. 2016;6(1):40-44. https://izlik.org/JA73TC67GC
Chicago
Özen, Mehmet, and Fatma Zehra Uzekmek. 2016. “MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING”. TOJSAT 6 (1): 40-44. https://izlik.org/JA73TC67GC.
EndNote
Özen M, Uzekmek FZ (July 1, 2016) MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING. TOJSAT 6 1 40–44.
IEEE
[1]M. Özen and F. Z. Uzekmek, “MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING”, TOJSAT, vol. 6, no. 1, pp. 40–44, July 2016, [Online]. Available: https://izlik.org/JA73TC67GC
ISNAD
Özen, Mehmet - Uzekmek, Fatma Zehra. “MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING”. TOJSAT 6/1 (July 1, 2016): 40-44. https://izlik.org/JA73TC67GC.
JAMA
1.Özen M, Uzekmek FZ. MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING. TOJSAT. 2016;6:40–44.
MLA
Özen, Mehmet, and Fatma Zehra Uzekmek. “MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING”. TOJSAT, vol. 6, no. 1, July 2016, pp. 40-44, https://izlik.org/JA73TC67GC.
Vancouver
1.Mehmet Özen, Fatma Zehra Uzekmek. MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING. TOJSAT [Internet]. 2016 Jul. 1;6(1):40-4. Available from: https://izlik.org/JA73TC67GC