@article {
author = {Sobhani, Reza},
title = {Gray isometries for finite $p$-groups},
journal = {Transactions on Combinatorics},
volume = {2},
number = {1},
pages = {17-26},
year = {2013},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2013.2762},
abstract = {We construct two classes of Gray maps, called type-I Gray map and type-II Gray map, for a finite $p$-group $G$. Type-I Gray maps are constructed based on the existence of a Gray map for a maximal subgroup $H$ of $G$. When $G$ is a semidirect product of two finite $p$-groups $H$ and $K$, both $H$ and $K$ admit Gray maps and the corresponding homomorphism $\psi:H\longrightarrow {\rm Aut}(K)$ is compatible with the Gray map of $K$ in a sense which we will explain, we construct type-II Gray maps for $G$. Finally, we consider group codes over the dihedral group $D_8$ of order 8 given by the set of their generators, and derive a representation and an encoding procedure for such codes.},
keywords = {Finite group,Code,Gray map,Isometry},
url = {https://toc.ui.ac.ir/article_2762.html},
eprint = {https://toc.ui.ac.ir/article_2762_9284f3f283a59b2d3778fed1f1d9bbfd.pdf}
}