We prove that the smallest cardinality of a maximal packing in any tree is at most the cardinality of an R-annihilated set. As a corollary to this result we point out that a set of parameters of trees involving packing, perfect neighbourhood, R-annihilated, irredundant and dominating sets is totally ordered. The class of trees for which all these parameters are equal is described and we give an...

In this correspondence, we propose some new designs of 2 2 unitary space-time codes of sizes 6; 32; 48; 64 with best known diversity products (or product distances) by partially using sphere packing theory. In particular, we present an optimal 2 2 unitary space-time code of size 6 in the sense that it reaches the maximal possible diversity product for 22 unitary space-time codes of size 6. The ...

Let ν+ and ν− be two measured laminations which fill up a hyperbolic surface. Kerckhoff [Duke Math. J. 65 (1992), 187–213] defines a line of minima as a family of surfaces where convex combinations of the hyperbolic length functions of ν+ and ν− are minimum. This is a proper curve in the Teichmüller space. We show that there exists a line of minima which does not converge in the Thurston compac...

We study properties of rank metric and codes in rank metric over finite fields. We show that perfect codes do not exist. We derive an equivalent of the Varshamov-Gilbert bound in Hamming metric. We study the asymptotic behavior of the minimum rank distance of codes that are on GV. We show that the packing density of maximum rank distance codes is lower bounded by a function depending on the err...

In this paper we introduce an evolutionary hyperheuristic approach to solve difficult strip packing problems. We have designed a genetic based hyperheuristic using the most recently proposed low-level heuristics in the literature. Two versions for tuning parameters have also been evaluated. The results obtained are very encouraging showing that our approach outperforms the single heuristics and...