MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING

MACWILLIAMS IDENTITIES OF LINEAR CODES OVER THE RING

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.

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  • 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.
TOJSAT-Cover
  • ISSN: 2146-7390
  • Başlangıç: 2011
  • Yayıncı: The association of science, education and technology