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Characters and cyclotomic fields in finite geometry

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 Ma...

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Detalles Bibliográficos
Autor principal: Schmidt, Bernhard
Lenguaje:eng
Publicado: Springer 2002
Materias:
Acceso en línea:https://dx.doi.org/10.1007/b84213
http://cds.cern.ch/record/1691433
Descripción
Sumario: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.