On Generalized Galois Cyclic Orbit Flag Codes

Clementa Alonso-González and Miguel Ángel Navarro-Pérez
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Clementa Alonso-González: Departement de Matemàtiques, Universitat d’Alacant, Ap. Correus 99, E-03080 Alacant, Spain
Miguel Ángel Navarro-Pérez: Departement de Matemàtiques, Universitat d’Alacant, Ap. Correus 99, E-03080 Alacant, Spain

Mathematics, 2022, vol. 10, issue 2, 1-25

Abstract: Flag codes that are orbits of a cyclic subgroup of the general linear group acting on flags of a vector space over a finite field, are called cyclic orbit flag codes . In this paper, we present a new contribution to the study of such codes, by focusing this time on the generating flag. More precisely, we examine those ones whose generating flag has at least one subfield among its subspaces. In this situation, two important families arise: the already known Galois flag codes , in case we have just fields, or the generalized Galois flag codes in other case. We investigate the parameters and properties of the latter ones and explore the relationship with their underlying Galois flag code.

Keywords: network coding; flag codes; cyclic orbit flag codes; Galois flags (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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