Cyclic orbit flag codes Articles uri icon

publication date

  • August 2021

start page

  • 231

end page

  • 2356

issue

  • 10

volume

  • 89

International Standard Serial Number (ISSN)

  • 0925-1022

abstract

  • In network coding, a flag code is a set of sequences of nested subspaces of Fnq
    , being Fq
    the finite field with q elements. Flag codes defined as orbits of a cyclic subgroup of the general linear group acting on flags of Fnq
    are called cyclic orbit flag codes. Inspired by the ideas in Gluesing-Luerssen et al. (Adv Math Commun 9(2):177-197, 2015), we determine the cardinality of a cyclic orbit flag code and provide bounds for its distance with the help of the largest subfield over which all the subspaces of a flag are vector spaces (the best friend of the flag). Special attention is paid to two specific families of cyclic orbit flag codes attaining the extreme possible values of the distance: Galois cyclic orbit flag codes and optimum distance cyclic orbit flag codes. We study in detail both classes of codes and analyze the parameters of the respective subcodes that still have a cyclic orbital structure

subjects

  • Mathematics

keywords

  • network coding; flag codes; cyclic orbit flag codes