orbit codes
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IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 17139-17147
Author(s):  
Shangdi Chen ◽  
Qin Xu
Keyword(s):  


2021 ◽  
Vol 608 ◽  
pp. 54-67
Author(s):  
Shangdi Chen ◽  
Junying Liang
Keyword(s):  


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Heide Gluesing-Luerssen ◽  
Hunter Lehmann

<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>



2020 ◽  
Vol 36 (4) ◽  
pp. 803-815
Author(s):  
Shang-di Chen ◽  
Jun-ying Liang
Keyword(s):  


2020 ◽  
Vol 14 (4) ◽  
pp. 631-650
Author(s):  
Gustavo Terra Bastos ◽  
◽  
Reginaldo Palazzo Júnior ◽  
Marinês Guerreiro ◽  
◽  
...  
Keyword(s):  


2019 ◽  
Vol 11 (05) ◽  
pp. 1950061
Author(s):  
Mahdieh Hakimi Poroch ◽  
Ali Asghar Talebi

Constant dimension subspace codes are subsets of the finite Grassmann Variety. Orbit codes are constant dimension subspace codes that arise as the orbit of subgroup of general linear group acting on subspaces in an ambient space. In particular, orbit codes of symplectic subgroup of the general linear group have been investigated recently. In this paper, we determine product of symplectic groups and its orbit code, and decoding algorithm of this code is considered.



2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Angela Aguglia ◽  
◽  
Antonio Cossidente ◽  
Giuseppe Marino ◽  
Francesco Pavese ◽  
...  


2018 ◽  
Vol 11 (5) ◽  
pp. 839-852
Author(s):  
Joan-Josep Climent ◽  
Verónica Requena ◽  
Xaro Soler-Escrivà
Keyword(s):  


2018 ◽  
Vol 960 ◽  
pp. 012004
Author(s):  
E C T Corro ◽  
J M T Lampos ◽  
H S Palines ◽  
V P Sison
Keyword(s):  


2017 ◽  
Vol 63 (11) ◽  
pp. 7616-7616
Author(s):  
Anna-Lena Horlemann-Trautmann ◽  
Felice Manganiello ◽  
Michael Braun ◽  
Joachim Rosenthal
Keyword(s):  


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