Classification Algorithms for Codes and Designs

This book considers one of the basic problems in discrete mathematics: given a collection of constraints, describe up to isomorphism all the objects that meet them. Only a handful of classification results for combinatorial objects are dated before the mid-20th century; indeed, it is through modern computers and recent developments in algorithms that this topic has flourished and matured. This book is the first comprehensive reference on combinatorial classification algorithms, with emphasis on both the general theory and application to central families of combinatorial objects, in particular, codes and designs.

Excellent interdisciplinary monograph on highly applications relevant topic Provides the first comprehensive reference on combinatorial classification algorithms Addresses both the general theory and application to central families of combinatorial objects

Contenu
Graphs, Designs, and Codes.- Representations and Isomorphism.- Isomorph-Free Exhaustive Generation.- Auxiliary Algorithms.- Classification of Designs.- Classification of Codes.- Classification of Related Structures.- Prescribing Automorphism Groups.- Validity of Computational Results.- Computational Complexity.- Nonexistence of Projective Planes of Order 10.