Cycle covering of binary matroids
Journal of Combinatorial Theory Series B
An “average distance” inequality for large subsets of the cube
Journal of Combinatorial Theory Series B
Maximal sets of given diameter in the grid and the torus
Discrete Mathematics
The asymptotic behaviour of diameters in the average
Journal of Combinatorial Theory Series B
On embedding complete graphs into hypercubes
Discrete Mathematics
On the average hamming distance for binary codes
Discrete Applied Mathematics
Covering cliques with spanning bicliques
Journal of Graph Theory
On the variance of average distance of subsets in the Hamming space
Discrete Applied Mathematics
Optimal hash functions for approximate matches on the n-cube
IEEE Transactions on Information Theory
| Hi-index | 0.11 |
In 1977, Ahlswede and Katona proposed the following isoperimetric problem: find a set S of n points in {0,1}k whose average Hamming distance is minimal--or equivalently find an n-vertex subgraph of the hypercube Qk whose average distance is minimal.We report on some recent results and conjecture that S can be chosen to be the set of all points in {0,1}k that are distance at most r from some point c ∈ Rk. We show that these "discrete balls" include all known good constructions and we provide additional evidence supporting the conjecture.