Another diametric theorem in Hamming spaces: optimal group anticodes

In the last century together with Levon Khachatrian we established a diametric theorem in Hamming space H
ⁿ
=(X
ⁿ
,d
H
). Now we contribute a diametric theorem for such spaces, if they are endowed with the group structure G
ⁿ
=
ⁿ
Σ
1
G, the direct sum of a group G on X={0,1,...,q-1}, and as candidates are considered subgroups of G
ⁿ
. For all finite groups G, every permitted distance d, and all n≥d subgroups of G
ⁿ
with diameter d have maximal cardinality q
^d
. Other extremal problems can also be studied in this setting.