Consider the graph with all permutations of a symbol sequence as vertices, where two permutations are connected by an edge when they differ by an interchange of two distinct adjacent symbols. In 1965, D. H. Lehmer conjectured that all vertices in this graph can be visited by a Hamiltonian path that is possibly imperfect , in the sense of having spurs . Such a spur visits a vertex twice, with a single vertex in-between. We prove Lehmer’s conjecture for binary permutations that involve only two distinct symbols. For general symbol sequences, we identify the stutter permutations as candidate spur tips, and prove that the non-stutter permutations admit a disjoint cycle cover. We also provide new (simpler) proofs for some known results.

Model comparison is an important challenge in model-driven engineering, with many application areas such as model versioning and domain model recovery. There are numerous techniques that address this challenge in the literature, ranging from graph-based to linguistic ones. Most of these involve pairwise comparison, which might work, e.g. for model versioning with a small number of models to consider. However, they mostly ignore the case where there is a large number of models to compare, such as in common domain model/metamodel recovery from multiple models. In this paper we present a generic approach for model comparison and analysis as an exploratory first step for model recovery. We propose representing models in vector space model, and applying clustering techniques to compare and analyse a large set of models. We demonstrate our approach on a synthetic dataset of models generated via genetic algorithms.

By means of local search techniques, five quasi-cyclic codes have been found that have a higher minimum distance than known binary linear codes. The new codes have parameters [102,17,37], [60,20,17], [84,21,27], [105,21,36], and [100,25,30]. Also, 39 other quasi-cyclic codes have been found that improve the parameter sets of previously known quasi-cyclic codes. Twenty-four of them give a new and easier description of binary linear codes with best known parameters.

Tables with lower and upper bounds for d/sub max/ (n,k), the maximum possible minimum distance of a binary linear code with word length n and dimension k, are shown.>

In 1973 Helgert and Sfinaff published a table of upper and lower bounds on the maximum minimum-distance for binary linear error-correcting codes up to length127. This article presents an updated table incorporating numerous improvements that have appeared since then. To simplify the updating task the author has developed a computer program that systematically investigates the consequences of each improvement by applying several well-known general code-construction techniques. This program also made it possible to check the original table. Furthermore, it offers a quick and reliable update service for future improvements.