is simplified. Upper bounds on the coding type problem, i.e. the determination of the maximum cardinality of a code consisting of unordered pairs of subsets far away from each other, are improved. The sphere packing problem, i.e. the determination of the maximum number of disjoint balls of a prescribed radius, is introduced and discussed. It is less closely connected to the first problem than it is in the most important spaces of coding theory.
Authors:Jörn Quistorff and Jan-Christoph Schlage-Puchta
We consider generalized surjective codes, together with their connection to covering codes and covering arrays. We prove new bounds on σq(n; s; r), the minimal cardinality of a q-ary code of length n, which is s-surjective with radius r. For covering codes we deduce the new records K6(10, 7) ≦ 18 and K6(9, 6) ≦ 24.