Equivalence for flag codes Articles uri icon

authors

  • NAVARRO PEREZ, MIGUEL ANGEL
  • SOLER-ESCRIVA, XARO

publication date

  • March 2024

start page

  • 1

end page

  • 26

volume

  • 690

International Standard Serial Number (ISSN)

  • 0024-3795

Electronic International Standard Serial Number (EISSN)

  • 1873-1856

abstract

  • Given a finite field Fq and a positive integer n, a flag is a sequence of nested Fq-subspaces of a vector space Fnq and a flag code is a nonempty collection of flags. The projected codes of a flag code are the constant dimension codes containing all the subspaces of prescribed dimensions that form the flags in the flag code. In this paper we address the notion of equivalence for flag codes and explore in which situations such an equivalence can be reduced to the equivalence of the corresponding projected codes. In addition, this study leads to new results concerning the automorphism group of certain families of flag codes, some of them also introduced in this paper.

subjects

  • Mathematics

keywords

  • flag codes; constant dimension code; (semi)linear equivalence; automorphism group