On the covering dimension of a linear code
On the covering dimension of a linear code
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关于线性码的覆盖维数
DOI：
10.1109/tit.2016.2538768
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Keisuke Shiromoto
中科院分区：
文献类型：
--
作者：
Thomas Britz;Keisuke Shiromoto
本文介绍了有限域上线性码的覆盖维数，它类似于可表示矩阵的临界指数，从而推广了编码理论中几个基本问题的核心不变量。证明了覆盖维数的上界，改进了龚氏临界指数的经典界。此外，还给出了在该覆盖维范围内达到相等的线性码的构造。
This paper introduces the covering dimension of a linear code over a finite field, which is analogous to the critical exponent of a representable matroid and, thus, generalizes invariants that lie at the heart of several fundamental problems in a coding theory. An upper bound on the covering dimension is proved, improving Kung's classical bound for the critical exponent. In addition, a construction is given for linear codes that attain equality in this covering dimension bound.