q-polymatroids and their relation to rank-metric codes
q-polymatroids and their relation to rank-metric codes
复制标题
q-polymaroids 及其与秩度量代码的关系
DOI：
10.1007/s10801-022-01129-y
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发表时间：
2021
影响因子：
0.8
通讯作者：
B. Jany
中科院分区：
文献类型：
--
作者：
H. Gluesing;B. Jany
众所周知，线性秩度量码会产生q-多拟阵。类似于拟阵理论，人们可能会问给定的q-多拟阵是否可以用秩度量码表示。我们提供了一个答案，提出了一个例子的aq-拟阵，这是不表示的任何线性秩度量码，并通过铺路拟阵的关系，提供的例子variousq-拟阵是不表示的线性秩度量码。然后，我们继续介绍删除和收缩的q-polymatroids，并表明它们是相互对偶的，并对应于穿孔和缩短的秩度量码。最后，我们引入了一个闭包算子沿着与平坦的概念，并证明了广义秩度量码的秩重量是完全由相关q-多拟阵的平坦。
It is well known that linear rank-metric codes give rise toq-polymatroids. Analogously to matroid theory, one may ask whether a givenq-polymatroid is representable by a rank-metric code. We provide an answer by presenting an example of aq-matroid that is not representable by any linear rank-metric code and, via a relation to paving matroids, provide examples of variousq-matroids that are not representable by-linear rank-metric codes. We then go on and introduce deletion and contraction forq-polymatroids and show that they are mutually dual and correspond to puncturing and shortening of rank-metric codes. Finally, we introduce a closure operator along with the notion of flats and show that the generalized rank weights of a rank-metric code are fully determined by the flats of the associatedq-polymatroid.
秩度量码的Wei型对偶定理
DOI：
10.1007/s10623-019-00688-9
发表时间：
2020
期刊：
Designs, Codes and Cryptography
影响因子：
--
作者：
Thomas Britz;Adam Mammoliti;Keisuke Shiromoto
通讯作者：
Keisuke Shiromoto