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- catalog 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.".
- catalog contributor b12662093.
- catalog created "c2002.".
- catalog date "2002".
- catalog date "c2002.".
- catalog dateCopyrighted "c2002.".
- catalog description "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.".
- catalog description "Includes bibliographical references (p. [91]-98) and index.".
- catalog description "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.".
- catalog extent "viii, 100 p. ;".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "354044243X (alk. paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1797.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1797".
- catalog issued "2002".
- catalog issued "c2002.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "510 s 516/.13 21".
- catalog subject "Combinatorics.".
- catalog subject "Cyclotomy.".
- catalog subject "Difference sets.".
- catalog subject "Finite geometries.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1797 QA167.2".
- catalog tableOfContents "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.".
- catalog title "Characters and cyclotomic fields in finite geometry / Bernhard Schmidt.".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".