The generic group model is a valuable methodology for analysing the computational hardness some number-theoretic problems used in cryptography. Although generic hardness proofs exhibit many similarities, still the computational intractability of every newly introduced problem needs to be proven from scratch, a task that can easily become complicated and cumbersome when done rigorously. In this ...

The paper considers an algebraic notion of automorphic equivalence of models and of multi-models. It is applied to the solution of the problem of informational equivalence of knowledge bases. We show that in the case of linear subjects of knowledge the problem can be reduced to the well-known in computational group theory problems about isomorphism and conjugacy of subgroups of a general linear...

We generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya Cab curves proposed by Lee, Bras-Amorós, and O’Sullivan [31] to general one-point AG codes, without any assumption. We also extend their unique decoding algorithm to list decoding, modify it so that it can be used with the Feng-Rao improved code construction, prove equality between its error correcting capa...

Index 74 Preface The three subjects of the title (codes, matroids, and permutation groups) have many interconnections. In particular, in each case, there is a polynomial which captures a lot of information about the structure: we have the weight enumerator of a code, the Tutte polynomial (or rank polynomial) of a matroid, and the cycle index of a permutation group. With any code is associated a...

We generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya Cab curves proposed by Lee, Bras-Amorós and O’Sullivan to general one-point AG codes, without any assumption. We also extend their unique decoding algorithm to list decoding, modify it so that it can be used with the Feng-Rao improved code construction, analyze its error correcting capability that has not b...

Branch and bound approaches for axial three-dimensional assignment problems are considered. Several branching schemes arising from facet deening inequalities are investigated. Further diierent bounding procedures are tested, such as reduction methods and bounds found by non-smooth nonlinear programming methods. The computational tests show that the classical branching on one variable together w...

Various subsets of self-avoiding walks naturally appear when investigating existing methods designed to predict the 3D conformation of a protein of interest. Two such subsets, namely the folded and the unfoldable self-avoiding walks, are studied computationally in this article. We show that these two sets are equal and correspond to the whole n-step self-avoiding walks for n≤14, but that they a...

This set of notes on GAP was prepared for a tutorial at ISSAC 2000 in St Andrews. This tutorial is intended neither to give an introduction to computational group theory, nor to be a replacement for a manual. Instead, I want to give ideas what can be done with the system and how I would tackle certain problems. Much of this is based on questions colleagues came up with over the last years. Whil...

Adding symmetry breaking constraints is one of the oldest ways of breaking variable symmetries for CSPs. For instance, it is well known that all the symmetries for the pigeon hole problem can be removed by ordering the variables. We have generalized this result to all CSPs where the variables are subject to an all different constraint. In such case it is possible to remove all variable symmetri...

A variety of elementary combinatorial techniques for permutation groups are reviewed. It is shown how to apply these techniques to yield faster and/or more space-efficient algorithms for problems including group membership, normal closure, center, base change and Cayley graphs. Emphasis is placed on randomized techniques and new data structures. The paper includes both a survey of recent algori...