7
votes
2answers
525 views

Automorphisms of subgroup of hamming cube under distance constraint

Let $S$ be a subset of $\{0,1\}^n$ such that any two elements of $S$ are at least (Hamming) distance 5 apart. I'm looking for an upper bound on the size of the automorphism group of $S$. There's a ...
1
vote
1answer
289 views

stabilizer always abelian? [closed]

Let G be a finite group acting on a finite dimensional vector space V. Let C be a nontrivial subspace of V. Let H be the subgroup of G that fixes C pointwise (the stabilizer of C). I'm fairly sure ...
1
vote
1answer
276 views

Large subgroups of the Hamming cube

Let's consider the abelian group $\mathbb{Z}^N_2$ equipped with the Hamming metric (the hypercube). Suppose I have a subgroup of this hypercube (not necessarily a subcube) which is generated by a set ...