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Askary, Soleyman; Biranvand, Nader; Shirjian, Farrokh

New constructions of orbit codes based on imprimitive wreath products and wreathed tensor products. (English) Zbl 07797012

Rend. Circ. Mat. Palermo (2) 73, No. 1, 85-98 (2024).
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 \({\mathbb{F}}^n_q\) under the action of some subgroup of the finite general linear group \(\mathrm{GL}_n(q)\). 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 [J.-J. Climent et al., Cryptogr. Commun. 11, No. 5, 839–852 (2019; Zbl 1419.94082)].

MSC:

94B60 Other types of codes

Keywords:

random linear network coding; algebraic coding theory; non-abelian orbit code; linear groups

Citations:

Zbl 1419.94082

Software:

OEIS
Cite Review PDF
Full Text: DOI

Online Encyclopedia of Integer Sequences:

Number of primitive permutation groups of degree n.

References:

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