Vector multispaces and multispace codes

Mladen Kovačević

Applied Mathematics and Computation, 2025, vol. 486, issue C

Abstract: 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.

Keywords: Multiset; Multispace; Projective space; Grassmannian; Linearized polynomial; Modular lattice; Subspace code; Random linear network coding (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:486:y:2025:i:c:s0096300324005022

DOI: 10.1016/j.amc.2024.129041

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