Advanced Search
Article Contents
Article Contents

Rank weights for arbitrary finite field extensions

  • * Corresponding author: Grégory Berhuy

    * Corresponding author: Grégory Berhuy 
Abstract Full Text(HTML) Related Papers Cited by
  • In this paper, we study several definitions of generalized rank weights for arbitrary finite extensions of fields. We prove that all these definitions coincide, generalizing known results for extensions of finite fields.

    Mathematics Subject Classification: Primary: 94C99; Secondary: 94B27, 94B60.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] D. Augot, P. Loidreau and G. Robert, Rank metric and Gabidulin codes in characteristic zero, in 2013 IEEE International Symposium on Information Theory, (2013), 509–513. doi: 10.1109/ISIT.2013.6620278.
    [2] S. Bosch, W. Lütkebohmert and M. Raynaud, Néron Models. Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 3, Springer-Verlag, Berlin, 1990. doi: 10.1007/978-3-642-51438-8.
    [3] B. Conrad, O. Gabber and G. Prasad, Pseudo-Reductive Groups, New Mathematical Monographs, Vol. 26, Cambridge University Press, Cambridge, 2015. doi: 10.1017/CBO9781316092439.
    [4] P. Delsarte, On subfield codes of modified Reed-Solomon codes, IEEE Trans. Inform. Theory IT-21, (1975), no. 5,575–576. doi: 10.1109/tit.1975.1055435.
    [5] J. Ducoat, Generalized rank weights: A duality statement. Topics in Finite Fields, in Contemporary Mathematics, Vol. 632, Amer. Math. Soc., Providence, RI, 2015,101–109. doi: 10.1090/conm/632/12622.
    [6] È. M. Gabidulin, Theory of codes of maximum rank distance, Problemy Peredachi Informatsii, 21 (1985), 3-16. 
    [7] M. Giorgetti and A. Previtali, Galois invariance, trace codes and subfield subcodes, Finite Fields Appl., 16 (2010), 96-99.  doi: 10.1016/j.ffa.2010.01.002.
    [8] A. Grothendieck, Éléments de géométrie algèbrique: Ⅱ. Étude globale élémentaire de quelques classes de morphismes, Inst. Hautes Études Sci. Publ. Math., 8 (1961), 5-222. 
    [9] R. Jurrius and G. R. Pellikaan, On defining generalized rank weights, Adv. Math. Commun., 11 (2017), 225-235.  doi: 10.3934/amc.2017014.
    [10] J. KuriharaR. Matsumoto and T. Uyematsu, Relative generalized rank weight of linear codes and its applications to network coding, IEEE Trans. Inform. Theory, 61 (2015), 3912-3936.  doi: 10.1109/TIT.2015.2429713.
    [11] F. Oggier and A. Sboui, On the existence of generalized rank weights, in 2012 IEEE International Symposium on Information Theory, (2012), 406–410.
    [12] B. Poonen, Rational Points on Varieties, Graduate Studies in Mathematics, Vol. 186, American Mathematical Society, Providence, RI, 2017.
  • 加载中

Article Metrics

HTML views(854) PDF downloads(266) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint