We give a non-constructive proof ot the existence of good coverings of binary and non binary Hamming spaces by spheres centered on a subspace (linear codes). The results hold for tiles other than spheres.
Sphere coverings of the hypercube with incomparable centers
✍ Scribed by Zoltán Füredi; Jeff Kahn; Daniel J. Kleitman
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 311 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
It is shown that the shadow of a Sperner family can cover 10 percent of the Boolean algebra. Whether this can be improved to (100 -o(l))% remains open. 1 a91 < c( J2) -=I C' 5 (l-1) holds for every Sperner family 97 This was disproved by Kospanov [8] who
📜 SIMILAR VOLUMES
An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity. This proves a conjecture of Goulden, Jackson, and Vainshtein for the explicit number of such cov
An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the double torus, with elementary branch points and prescribed ramification type over infinity. Thus we are able to determine various linear recurrence equations for the numbers of thes