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Designs, Codes and Cryptography

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28.08.2021

Cyclic orbit flag codes

verfasst von: Clementa Alonso-González, Miguel Ángel Navarro-Pérez

Erschienen in: Designs, Codes and Cryptography | Ausgabe 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.

Vorheriger Artikel Vectorial bent functions and partial difference sets

Nächster Artikel Public key encryption with filtered equality test revisited

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Titel: Cyclic orbit flag codes
verfasst von: Clementa Alonso-González
Miguel Ángel Navarro-Pérez
Publikationsdatum: 28.08.2021
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 10/2021
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-021-00920-5

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