We consider weighted Reed-Muller codes over point ensemble S1 × · · · × Sm where Si needs not be of the same size as Sj . For m = 2 we determine optimal weights and analyze in detail what is the impact of the ratio |S1|/|S2| on the minimum distance. In conclusion the weighted Reed-Muller code construction is much better than its reputation. For a class of affine variety codes that contains the ...

THE major broad achievements by the luminaries concept of genetic load (Haldane 1937; Muller 1950; Crow 1993). Other essays in the Perspectives series that of science often distract from our appreciation of their significant but narrower contributions to allied refer to Muller are Paul (1988), Lederberg (1991), Crow (1992), and Crow and Abrahamson (1997). fields. One example is Linus Pauling’s ...

We consider the complexity of infinite games played on finite graphs. We establish a framework in which the expressiveness and succinctness of different types of winning conditions can be compared. We show that the problem of deciding the winner in Muller games is Pspace-complete. This is then used to establish Pspacecompleteness for Emerson-Lei games and for games described by Zielonka DAGs. A...

We transform a Muller game with n vertices into a safety game with (n!)3 vertices whose solution allows to determine the winning regions of the Muller game and to compute a finite-state winning strategy for one player. This yields a novel antichain-based memory structure and a natural notion of permissive strategies for Muller games. Moreover, we generalize our construction by presenting a new ...