论文标题
Butson-Hadamard矩阵和Plotkin-timal-timal p^k-ary代码
Butson-Hadamard matrices and Plotkin-optimal p^k-ary codes
论文作者
论文摘要
Butson-Hadamard矩阵H是维度为N的正方形矩阵，其条目是统一的复杂根，因此HH*= Ni。在这项工作的第一部分中，研究了广义灰色地图的一些新结果。在第二部分中，证明了这些代码从Butson-Hadamard矩阵获得的代码以及这些代码最小距离的一些界限。特别是，我们表明，从Butson-Hadamard矩阵获得的代码在非均匀的重量下与Plotkin结合。我们还提供了某些代码族的参数，这些代码家族是根据（非）均匀灰色地图下修改的Butson-Hadamard矩阵获得的。
A Butson-Hadamard matrix H is a square matrix of dimension n whose entries are complex roots of unity such that HH*= nI. In the first part of this work, some new results on generalized Gray map are studied. In the second part, codes obtained from Butson-Hadamard matrices and some bounds on the minimum distance of these codes are proved. In particular, we show that the code obtained from a Butson-Hadamard matrix meets the Plotkin bound under a non-homogeneous weight. We also give the parameters of some code families which are obtained from modified Butson-Hadamard matrices under a (non)homogeneous Gray map.
