Graphs, Codes, and Designs

The package GRAPE allows one to construct graphs (with or without using groups), to determine many invariants of graphs, to classify complete subgraphs with various properties, to determine automorphism groups of graphs, and to test graph isomorphism (the last two via an interface to B.D. McKay’s nauty package). A special feature of this package is the use of (subgroups of) the automorphism group of a graph (and hence of permutation group methods) to reduce the store required for many graphs and to reduce the time taken by many graph-theoretical algorithms.

The package GUAVA can construct many classes of codes, derive invariants such as minimal distance and weight distribution and find their automorphism groups.

The package Design provides classification, partitioning, and study of block designs, including the determination of automorphism groups, the testing of isomorphism, and the calculation of statistical efficiency measures of 1-designs using exact methods.

The package RDS provides functions for the complete enumeration and construction of relative difference sets and the corresponding projective planes. The constructed planes can be analysed using the Design package.