Vector Multispaces and Multispace Codes
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909301803581440 |
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| author | Kovačević, Mladen |
| author_facet | Kovačević, Mladen |
| contents | 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 $ \mathbb{F}_q^n $) 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 $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14312 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Vector Multispaces and Multispace Codes Kovačević, Mladen Information Theory Discrete Mathematics Combinatorics 15A03, 94B25, 05E16, 06B99 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 $ \mathbb{F}_q^n $) 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 $. |
| title | Vector Multispaces and Multispace Codes |
| topic | Information Theory Discrete Mathematics Combinatorics 15A03, 94B25, 05E16, 06B99 |
| url | https://arxiv.org/abs/2312.14312 |