Note: a new lower bound for the football pool problem for six matches
Journal of Combinatorial Theory Series A
New Results on Codes with Covering Radius 1 and Minimum Distance 2
Designs, Codes and Cryptography
Improving Bounds on the Football Pool Problem by Integer Programming and High-Throughput Computing
INFORMS Journal on Computing
On the minimum size of 4-uniform hypergraphs without property B
Discrete Applied Mathematics
| Hi-index | 754.84 |
The minimum number of codewords in a binary code with length n and covering radius R is denoted by K(n, R). The values of K(n, 1) are known up to length 8, and the corresponding optimal codes have been classified. It is known that 57⩽K(9, 1)⩽62. In the current work, the lower bound is improved to settle K(9, 1)=62. In the approach, which is computer-aided, possible distributions of codewords in subspaces are refined until each subspace is of dimension zero (consists of only one word). Repeatedly, a linear programming problem is solved considering only inequivalent distributions. A connection between this approach and weighted coverings is also presented; the computations give new results for such coverings as a by-product