Vector multispaces and multispace codes

IF 4.3 3区 材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
Mladen Kovačević
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引用次数: 0

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.

矢量多空间和多空间代码
推导了允许单个向量的乘数大于 1 的有限向量空间的基本代数和组合性质。通过说明这里介绍的多空间编码可用于随机线性网络编码场景,它们概括了标准子空间编码(定义在 Fqn 的所有子空间集合中),并将其扩展到无限大的参数集,从而说明了多空间编码在编码理论中的应用。特别是,与子空间编码相反,对于任何固定的 n 和 q,都存在任意大的心数和最小距离的多空间编码。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
7.20
自引率
4.30%
发文量
567
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