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

By: Kaski, Petteri [author.]
Contributor(s): Östergård, Patric R.J [author.] | SpringerLink (Online service)
Material type: TextTextSeries: Algorithms and Computation in Mathematics: 15Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006Description: XI, 412 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540289913Subject(s): Mathematics | Coding theory | Computer mathematics | Combinatorics | Electrical engineering | Mathematics | Combinatorics | Computational Mathematics and Numerical Analysis | Coding and Information Theory | Communications Engineering, Networks | Signal, Image and Speech ProcessingAdditional physical formats: Printed edition:: No titleDDC classification: 511.6 LOC classification: QA164-167.2Online 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: A new starting-point and a new method are requisite, to insure a complete [classi?cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di?cult execution und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and H. S. White (1917) [129] The history of classifying combinatorial objects is as old as the history of the objects themselves. In the mid-19th century, Kirkman, Steiner, and others became the fathers of modern combinatorics, and their work – on various objects, including (what became later known as) Steiner triple systems – led to several classi?cation results. Almost a century earlier, in 1782, Euler [180] published some results on classifying small Latin squares, but for the ?rst few steps in this direction one should actually go at least as far back as ancient Greece and the proof that there are exactly ?ve Platonic solids. One of the most remarkable achievements in the early, pre-computer era is the classi?cation of the Steiner triple systems of order 15, quoted above. An onerous task that, today, no sensible person would attempt by hand calcu- tion. Because, with the exception of occasional parameters for which com- natorial arguments are e?ective (often to prove nonexistence or uniqueness), classi?cation in general is about algorithms and computation.
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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.

A new starting-point and a new method are requisite, to insure a complete [classi?cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di?cult execution und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and H. S. White (1917) [129] The history of classifying combinatorial objects is as old as the history of the objects themselves. In the mid-19th century, Kirkman, Steiner, and others became the fathers of modern combinatorics, and their work – on various objects, including (what became later known as) Steiner triple systems – led to several classi?cation results. Almost a century earlier, in 1782, Euler [180] published some results on classifying small Latin squares, but for the ?rst few steps in this direction one should actually go at least as far back as ancient Greece and the proof that there are exactly ?ve Platonic solids. One of the most remarkable achievements in the early, pre-computer era is the classi?cation of the Steiner triple systems of order 15, quoted above. An onerous task that, today, no sensible person would attempt by hand calcu- tion. Because, with the exception of occasional parameters for which com- natorial arguments are e?ective (often to prove nonexistence or uniqueness), classi?cation in general is about algorithms and computation.

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