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: Characters and Cyclotomic Fields in Finite Geometry
  name:
    name part: Schmidt, Bernhard.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2002
    edition: 1st ed. 2002.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 108 p. online resource.
  abstract: This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13<1<4x10^(12). Finally, a conjecturally complete classification of all irreducible cyclic two-weight codes is obtained.
  table of contents: 1. Introduction: The nature of the problems -- The combinatorial structures in question -- Group rings, characters, Fourier analysis -- Number theoretic tools -- Algebraic-combinatorial tools. 2. The field descent: The fixing theorem -- Prescribed absolute value -- Bounding the absoute value -- The modulus equation and the class group. 3. Exponent bounds: Self-conjugacy exponent bounds -- Field descent exponent bounds. 4. Two-weight irreducible cyclic bounds: A necessary and sufficient condition -- All two-weight irreducible cyclic codes?- Partial proof of Conjecture 4.2.4 -- Two-intersection sets and sub-difference sets.
  note: by Bernhard Schmidt.
  subject:
    topic: Combinatorics
  subject:
    topic: Combinatorics
  classification: QA164-167.2
  classification: 511.6
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 1797
  identifier: 9783540457978
  identifier: https://doi.org/10.1007/b84213
  record info:
    record creation date: 121227
    record change date: 20190619193806.0
    record identifier: 978-3-540-45797-8