rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Classification Algorithms for Codes and Designs
  name:
    name part: Kaski, Petteri.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Östergård, Patric R.J.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2006
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XI, 412 p. online resource.
  abstract: 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.
  table of 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.
  note: by Petteri Kaski, Patric R.J. Östergård.
  subject:
    topic: Mathematics
  subject:
    topic: Coding theory
  subject:
    topic: Computer mathematics
  subject:
    topic: Combinatorics
  subject:
    topic: Electrical engineering
  subject:
    topic: Mathematics
  subject:
    topic: Combinatorics
  subject:
    topic: Computational Mathematics and Numerical Analysis
  subject:
    topic: Coding and Information Theory
  subject:
    topic: Communications Engineering, Networks
  subject:
    topic: Signal, Image and Speech Processing
  classification: QA164-167.2
  classification: 511.6
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Algorithms and Computation in Mathematics, 15
  identifier: 9783540289913
  identifier: http://dx.doi.org/10.1007/3-540-28991-7
  record info:
    record creation date: 100301
    record change date: 20151204181331.0
    record identifier: 978-3-540-28991-3