Vector multispaces and multispace codes

Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than 1 are derived. An application in coding theory is illustrated by showing that multispace codes that are introduced here may be used in random linear network...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 486; p. 129041
Main Author: Kovačević, Mladen
Format: Journal Article
Language:English
Published: Elsevier Inc 01.02.2025
Subjects:
Grassmannian
Linearized polynomial
Modular lattice
Multiset
Multispace
Projective space
Random linear network coding
Subspace code
secondary
Modular lattice
Multispace
Grassmannian
Multiset
Subspace code
Random linear network coding
primary
Projective space
Linearized polynomial
ISSN:0096-3003
Online Access:Get full text
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Summary:Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than 1 are derived. An application in coding theory is illustrated by showing that multispace codes that are introduced here may be used in random linear network coding scenarios, and that they generalize standard subspace codes (defined in the set of all subspaces of Fqn) and extend them to an infinitely larger set of parameters. In particular, in contrast to subspace codes, multispace codes of arbitrarily large cardinality and minimum distance exist for any fixed n and q.
ISSN:0096-3003
DOI:10.1016/j.amc.2024.129041