New constructions of orbit codes based on imprimitive wreath products and wreathed tensor products

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 F q n under the action of some subgroup of the finite general linear group GL n ( q ) . The aim of this paper...

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Bibliographic Details
Published in:Rendiconti del Circolo matematico di Palermo Vol. 73; no. 1; pp. 85 - 98
Main Authors: Askary, Soleyman, Biranvand, Nader, Shirjian, Farrokh
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.02.2024
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Linear groups
94B05
Non-Abelian orbit code
Algebraic coding theory
Primary 11T71
94A60
Random linear network coding
ISSN:0009-725X, 1973-4409
Online Access:Get full text
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Summary: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 F q n under the action of some subgroup of the finite general linear group 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).
ISSN:0009-725X
1973-4409
DOI:10.1007/s12215-023-00903-6