most recent 30 from http://mathoverflow.net 2013-05-25T21:14:15Z http://mathoverflow.net/feeds/user/27235 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109635/automorphisms-of-subgroup-of-hamming-cube-under-distance-constraint rishig 2012-10-14T18:27:27Z 2013-05-24T17:22:00Z

<p>Let $S$ be a subset of <code>$\{0,1\}^n$</code> 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 $S$.</p> <p>There's a trivial upper bound of $2^nn!$ (the number of automorphisms of <code>$\{0,1\}^n$</code>), and an easy lower bound of $2^{n/5}(n/5)!$ (take S to be all elements of the form $xxxxx$, where $x$ is a bitstring of length $n/5$). </p> <p>Any bound of the form $n!/n^{cn}$ for any $c>0$ would be helpful.</p>

http://mathoverflow.net/questions/109635/automorphisms-of-subgroup-of-hamming-cube-under-distance-constraint rishig 2012-10-19T06:23:06Z 2012-10-19T06:23:06Z

Thanks for the comment. Haven't found anything yet that I've gotten to work, but I'll post here if I do.

http://mathoverflow.net/questions/109635/automorphisms-of-subgroup-of-hamming-cube-under-distance-constraint/109898#109898 rishig 2012-10-19T04:44:51Z 2012-10-19T04:44:51Z

Thanks for your response. I'm referring to automorphisms of the hypercube [1], which are substantially more restricted than $F_2^n$. For instance the linear map [[1 1] [1 0]] is an automorphism of $F_2^2$ but not of the square. [1] <a href="http://en.wikipedia.org/wiki/Hyperoctahedral_group" rel="nofollow">en.wikipedia.org/wiki/Hyperoctahedral_group</a>