A characterization of cyclic subspace codes via subspace polynomials

Zhao, Wei; Tang, Xilin

doi:10.1016/j.ffa.2019.01.002

Cited by 26 publications

(17 citation statements)

References 10 publications

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“…First examples of cyclic orbit codes with good distance appeared already in [7], and in fact, in most of the literature, cyclic orbit codes have been studied in this setting, see for instance [10] for details on the orbit length and some distance results, [1,17,18,3,21] for constructions of unions of cyclic orbit codes with good distance with the aid of subspace polynomials and [9] for a study of the distance distribution of cyclic orbit codes. The aforementioned unions of cyclic orbit codes are in fact orbits codes under the normalizer of F * q n in GL n (q).…”

Section: Introductionmentioning

confidence: 99%

Automorphism groups and isometries for cyclic orbit codes

Gluesing-Luerssen¹,

Lehmann²

2023

AMC

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<p style='text-indent:20px;'>We study orbit codes in the field extension <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_{q^n} $\end{document}</tex-math></inline-formula>. First we show that the automorphism group of a cyclic orbit code is contained in the normalizer of the Singer subgroup if the orbit is generated by a subspace that is not contained in a proper subfield of <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{F}_{q^n} $\end{document}</tex-math></inline-formula>. We then generalize to orbits under the normalizer of the Singer subgroup. In that situation some exceptional cases arise and some open cases remain. Finally we characterize linear isometries between such codes.</p>

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Section: Introductionmentioning

confidence: 99%

Automorphism groups and isometries for cyclic orbit codes

Gluesing-Luerssen¹,

Lehmann²

2023

AMC

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“…This family of codes has awaken a lot of interest due to the simplicity of their algebraic structure and to the existence of efficient encoding/decoding algorithms. We refer the reader to [5,6,8,9,10,19,21,23,24,26] for some of the more recent papers.…”

Section: Introductionmentioning

confidence: 99%

Cyclic orbit flag codes

Alonso-González

Navarro-Pérez

2021

Des. Codes Cryptogr.

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In network coding, a flag code is a set of sequences of nested subspaces of F n q , being 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 F n q are called cyclic orbit flag codes. Inspired by the ideas in [10], 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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“…, q n − 2}, where ω is a primitive element of F q n . First examples of cyclic orbit codes with good distance appeared already in [7], and in fact, in most of the literature, cyclic orbit codes have been studied in this setting, see for instance [10] for details on the orbit length and some distance results, [1,17,18,3,21] for constructions of unions of cyclic orbit codes with good distance with the aid of subspace polynomials and [9] for a study of the distance distribution of cyclic orbit codes. The aforementioned unions of cyclic orbit codes are in fact orbits codes under the normalizer of F * q n in GL n (q).…”

Section: Introductionmentioning

confidence: 99%

Automorphism Groups and Isometries for Cyclic Orbit Codes

Gluesing-Luerssen¹,

Lehmann²

2021

Preprint

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We study orbit codes in the field extension F q n . First we show that the automorphism group of a cyclic orbit code is contained in the normalizer of the Singer subgroup if the orbit is generated by a subspace that is not contained in a proper subfield of F q n . We then generalize to orbits under the normalizer of the Singer subgroup. In that situation some exceptional cases arise and some open cases remain. Finally we characterize linear isometries between such codes.

show abstract

A characterization of cyclic subspace codes via subspace polynomials

Cited by 26 publications

References 10 publications

Automorphism groups and isometries for cyclic orbit codes

Automorphism groups and isometries for cyclic orbit codes

Cyclic orbit flag codes

Automorphism Groups and Isometries for Cyclic Orbit Codes

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