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Classification Algorithms for Codes and Designs [electronic resource] /by Petteri Kaski, Patric R.J. Östergård.

by Kaski, Petteri [author.]; Östergård, Patric R.J [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Algorithms and Computation in Mathematics: 15Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.Description: XII, 412p. 62 illus. online resource.ISBN: 9783540289913.Subject(s): Mathematics | Coding theory | Computer science -- Mathematics | Combinatorics | Telecommunication | Mathematics | Combinatorics | Computational Mathematics and Numerical Analysis | Coding and Information Theory | Communications Engineering, Networks | Signal, Image and Speech ProcessingDDC classification: 511.6 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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. The book will be of great interest to researchers and can be used as course material for graduate courses in both computer science and mathematics.
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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.

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. The book will be of great interest to researchers and can be used as course material for graduate courses in both computer science and mathematics.

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