Another diametric theorem in Hamming spaces: optimal group anticodes

Abstract

In the last century together with Levon Khachatrian we established a diametric theorem in Hamming space Hⁿ=(Xⁿ,dH). Now we contribute a diametric theorem for such spaces, if they are endowed with the group structure Gⁿ=ⁿΣ1G, the direct sum of a group G on X={0,1,...,q-1}, and as candidates are considered subgroups of Gⁿ. For all finite groups G, every permitted distance d, and all n≥d subgroups of Gⁿwith diameter d have maximal cardinality q^d. Other extremal problems can also be studied in this setting.