The remoteness of the permutation code of the group $U_{6n}$

Document Type : Research Paper


Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran


Recently, a new parameter of a code, referred to as the remoteness, has been introduced.
This parameter can be viewed as a dual to the covering radius. It is exactly determined for the cyclic and dihedral groups. In this paper, we consider the group $U_{6n}$ as a subgroup of $S_{2n+3}$ and obtain its remoteness.  We show that the remoteness of the permutation code $U_{6n}$ is $2n+2$.  Moreover, it is proved that the covering radius of $U_{6n}$ is also $2n+2$.


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