Coverart for item
The Resource Characters and cyclotomic fields in finite geometry, Bernhard Schmidt

Characters and cyclotomic fields in finite geometry, Bernhard Schmidt

Label
Characters and cyclotomic fields in finite geometry
Title
Characters and cyclotomic fields in finite geometry
Statement of responsibility
Bernhard Schmidt
Creator
Subject
Language
eng
Summary
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 Rysers̀ 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
Member of
Cataloging source
COO
http://library.link/vocab/creatorDate
1967-
http://library.link/vocab/creatorName
Schmidt, Bernhard
Dewey number
  • 510 s
  • 516/.13
Index
index present
Language note
English
LC call number
  • QA3
  • QA167.2
LC item number
.L28 no. 1797
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Lecture notes in mathematics,
Series volume
1797
http://library.link/vocab/subjectName
  • Finite geometries
  • Difference sets
  • Cyclotomy
  • Cyclotomy
  • Difference sets
  • Finite geometries
Label
Characters and cyclotomic fields in finite geometry, Bernhard Schmidt
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 91-98) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
50993306
Dimensions
unknown
Extent
1 online resource (viii, 100 pages).
Form of item
online
Isbn
9783540457978
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/b84213.
Specific material designation
remote
System control number
(OCoLC)50993306
Label
Characters and cyclotomic fields in finite geometry, Bernhard Schmidt
Publication
Bibliography note
Includes bibliographical references (pages 91-98) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
50993306
Dimensions
unknown
Extent
1 online resource (viii, 100 pages).
Form of item
online
Isbn
9783540457978
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/b84213.
Specific material designation
remote
System control number
(OCoLC)50993306

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