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 qd. Other extremal problems can also be studied in this setting.
展开▼
机译：在上个世纪，我们与Levon Khachatrian一起在汉明空间H n =（X n ，d H ）中建立了一个直径定理。现在，如果为此类空间赋予了群结构G n = n Σ 1 G，则直接为它们建立一个直径定理X = {0,1，...，q-1}上的组G的一个子集，作为候选者被视为G n 的子组。对于所有有限群G，每个允许的距离d，以及直径 n 的所有n≥d个子群具有最大基数q d 。在这种情况下，也可以研究其他极端问题。
展开▼
