Advanced Search
Article Contents
Article Contents

Codes over local rings of order 16 and binary codes

Abstract Related Papers Cited by
  • We study codes over the commutative local Frobenius rings of order 16 with maximal ideals of size 8. We define a weight preserving Gray map and study the images of these codes as binary codes. We study self-dual codes and determine when they exist.
    Mathematics Subject Classification: Primary: 11T71, 94B05; Secondary: 13H99.


    \begin{equation} \\ \end{equation}
  • [1]

    J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE-IT, 36 (1990), 1319-1333.doi: 10.1109/18.59931.


    S. T. Dougherty and C. Fernandez-Cordoba, Codes over $\mathbbZ_{2^k}$, Gray maps and self-dual codes, Adv. Math. Commun., 5 (2011), 571-588.doi: 10.3934/amc.2011.5.571.


    S. T. Dougherty, P. Gaborit, M. Harada, A. Munemasa and P. Solé, Type IV self-dual codes over rings, IEEE-IT, 45 (1999), 2345-2360.doi: 10.1109/18.796375.


    S. T. Dougherty, J. L. Kim, H. Kulosman and H. Liu, Self-dual codes over Frobenius rings, Finite Fields Appl., 16 (2010), 14-26.doi: 10.1016/j.ffa.2009.11.004.


    S. T. Dougherty and H. Liu, Independence of vectors in codes over rings, Des. Codes Crypt., 51 (2009), 55-68.doi: 10.1007/s10623-008-9243-1.


    S. T. Dougherty and K. Shiromoto, Maximum distance codes over rings of order 4, IEEE-IT, 47 (2001), 400-404.doi: 10.1109/18.904544.


    S. T. Dougherty, B. Yildiz and S. Karadeniz, Codes over $R_k$, Gray maps and their binary images, Finite Fields Appl., 17 (2011), 205-219.doi: 10.1016/j.ffa.2010.11.002.


    A. R. Hammons Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé, The $Z_4$-linearity of Kerdock, Preparata, Goethals and related codes, IEEE-IT, 40 (1994), 301-319.doi: 10.1109/18.312154.


    F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.


    E. Martinez-Moro and S. Szabo, On codes over local Frobenius non-chain rings of order 16, Contemp. Math., 634 (2015), 227-242doi: 10.1090/conm/634/12702.


    J. Wood, Duality for modules over finite rings and applications to coding theory, Amer. J. Math., 121 (1999), 555-575.


    B. Yildiz and S. Karadeniz, Linear codes over $\mathbbF_2 + u \mathbbF_2 + v \mathbbF_2 + uv \mathbbF_2$, Des. Codes Crypt., 54 (2010), 61-81.doi: 10.1007/s10623-009-9309-8.


    B. Yildiz and S. Karadeniz, A new construction for the extended binary Golay code, Appl. Math. Inf. Sci., 8 (2014), 69-72.doi: 10.12785/amis/080107.


    B. Yildiz and S. Karadeniz, Linear codes over $\mathbbZ_4 + u \mathbbZ_4$, MacWilliams identities, projections, and formally self-dual codes, Finite Fields Appl., 27 (2014), 24-40.doi: 10.1016/j.ffa.2013.12.007.

  • 加载中

Article Metrics

HTML views() PDF downloads(489) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint