Navarro-Pérez, Miguel Ángel, Soler-Escrivà, Xaro
Equivalence for flag codes
Linear Algebra and its Applications. 2024, 690: 1-26. https://doi.org/10.1016/j.laa.2024.03.003
URI: http://hdl.handle.net/10045/141556
DOI: 10.1016/j.laa.2024.03.003
ISSN: 0024-3795 (Print)
Abstract: 
Given a finite field Fq and a positive integer n, a flagis 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.
Keywords:Flag codes, Constant dimension code, (Semi)linear equivalence, Automorphism group
Elsevier
info:eu-repo/semantics/article