Abstract
Orbit codes, as special constant dimension codes, have attracted much attention due to their applications for error correction in random network coding. They arise as orbits of a subspace of \({\mathbb {F}}^n_q\) under the action of some subgroup of the finite general linear group \(\textrm{GL}_n(q)\). The aim of this paper is to present constructions of large non-Abelian orbit codes having the maximum possible distance. The properties of imprimitive wreath products and wreathed tensor products of groups are employed to select certain types of subspaces and their stabilizers, thereby providing a systematic way of constructing orbit codes with optimum parameters. We also present explicit examples of such constructions which improve the parameters of the construction already obtained in Climent et al. (Cryptogr Commun 11:839-852, 2019).
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The authors would like to thank the anonymous referee for careful reading of the manuscript and providing invaluable and precise comments which improved the exposition of the paper significantly.
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Askary, S., Biranvand, N. & Shirjian, F. New constructions of orbit codes based on imprimitive wreath products and wreathed tensor products. Rend. Circ. Mat. Palermo, II. Ser 73, 85–98 (2024). https://doi.org/10.1007/s12215-023-00903-6
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DOI: https://doi.org/10.1007/s12215-023-00903-6