BibTex RIS Cite

MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING

Year 2016, Volume: 6 Issue: 1, 40 - 44, 23.07.2016

Mehmet Özen Fatma Zehra Uzekmek

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

Weight enumerator MacWillims identities

References

  • S.T. Dougherty, P. Gaborit, M. Harada & P. Sole (1999). Type II Codes over F2 uF2 Theory, 45, 32-45.
  • B. Yildiz & S. Karadeniz (2014). Linear Codes over ] u]: Macwilliams Identities, Projections and Formally
  • 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.
  • R.K. Bandi &M. Baintwal, Codes over ] , IEEE. u], IEEE. B. Yildiz & S. Karadeniz (2010). Linear Codes over F2 uF2 vF2 uvF2
  • J. Gao (2015). Some Results on Linear Codes over F p uFp u Fp, J. Appl. Math. Comput., 47:473-485.
  • A.R. Hammons, P.V/ Kumar, A.R. Calderbank, N.J.A. Sloane & P. Sole (1994). The ]
  • Linearity of Kerdock, Preparata, Goethals and Related Codes, IEEE Transactions on Information Theory, Vol. 40, No.2, pp. 301-319.

Year 2016, Volume: 6 Issue: 1, 40 - 44, 23.07.2016

Mehmet Özen Fatma Zehra Uzekmek

Abstract

References

  • S.T. Dougherty, P. Gaborit, M. Harada & P. Sole (1999). Type II Codes over F2 uF2 Theory, 45, 32-45.
  • B. Yildiz & S. Karadeniz (2014). Linear Codes over ] u]: Macwilliams Identities, Projections and Formally
  • 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.
  • R.K. Bandi &M. Baintwal, Codes over ] , IEEE. u], IEEE. B. Yildiz & S. Karadeniz (2010). Linear Codes over F2 uF2 vF2 uvF2
  • J. Gao (2015). Some Results on Linear Codes over F p uFp u Fp, J. Appl. Math. Comput., 47:473-485.
  • A.R. Hammons, P.V/ Kumar, A.R. Calderbank, N.J.A. Sloane & P. Sole (1994). The ]
  • Linearity of Kerdock, Preparata, Goethals and Related Codes, IEEE Transactions on Information Theory, Vol. 40, No.2, pp. 301-319.
There are 7 citations in total.

Details

Other ID JA56CK68TR
Journal Section Articles
Authors

Mehmet Özen This is me

Fatma Zehra Uzekmek This is me

Publication Date July 23, 2016
Published in Issue Year 2016 Volume: 6 Issue: 1

Cite

APA Özen, M., & Uzekmek, F. Z. (2016). MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING. TOJSAT, 6(1), 40-44.
AMA Özen M, Uzekmek FZ. MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING. TOJSAT. July 2016;6(1):40-44.
Chicago Özen, Mehmet, and Fatma Zehra Uzekmek. “MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING”. TOJSAT 6, no. 1 (July 2016): 40-44.
EndNote Özen M, Uzekmek FZ (July 1, 2016) MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING. TOJSAT 6 1 40–44.
IEEE M. Özen and F. Z. Uzekmek, “MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING”, TOJSAT, vol. 6, no. 1, pp. 40–44, 2016.
ISNAD Özen, Mehmet - Uzekmek, Fatma Zehra. “MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING”. TOJSAT 6/1 (July 2016), 40-44.
JAMA 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, 2016, pp. 40-44.
Vancouver Özen M, Uzekmek FZ. MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING. TOJSAT. 2016;6(1):40-4.