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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 10/2021

28-08-2021

Cyclic orbit flag codes

Authors: Clementa Alonso-González, Miguel Ángel Navarro-Pérez

Published in: Designs, Codes and Cryptography | Issue 10/2021

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Abstract

In network coding, a flag code is a set of sequences of nested subspaces of \({{\mathbb {F}}}_q^n\), being \({{\mathbb {F}}}_q\) the finite field with q elements. Flag codes defined as orbits of a cyclic subgroup of the general linear group acting on flags of \({{\mathbb {F}}}_q^n\) 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.
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Metadata
Title
Cyclic orbit flag codes
Authors
Clementa Alonso-González
Miguel Ángel Navarro-Pérez
Publication date
28-08-2021
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 10/2021
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-021-00920-5

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