TY  - BOOK
AU  - Schmidt,Bernhard
ED  - SpringerLink (Online service)
TI  - Characters and Cyclotomic Fields in Finite Geometry
T2  - Lecture Notes in Mathematics,
SN  - 9783540457978
AV  - QA164-167.2 
U1  - 511.6 23
PY  - 2002///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Combinatorics
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/b84213
ER  -