8 research outputs found
Remarks on a cyclotomic sequence
We analyse a binary cyclotomic sequence constructed via generalized cyclotomic classes by Bai et al. (IEEE Trans Inforem Theory 51: 1849-1853, 2005). First we determine the linear complexity of a natural generalization of this binary sequence to arbitrary prime fields. Secondly we consider k-error linear complexity and autocorrelation of these sequences and point out certain drawbacks of this construction. The results show that the parameters for the sequence construction must be carefully chosen in view of the respective application
A general approach to construction and determination of the linear complexity of sequences based on cosets
We give a general approach to -periodic sequences over a finite field \F_q constructed via a subgroup of the group of invertible elements modulo . Well known examples are Legendre sequences or the two-prime generator. For some generalizations of sequences considered in the literature and for some new examples of sequence constructions we determine the linear complexity
Four-manifolds, geometries and knots
The goal of this book is to characterize algebraically the closed 4-manifolds
that fibre nontrivially or admit geometries in the sense of Thurston, or which
are obtained by surgery on 2-knots, and to provide a reference for the topology
of such manifolds and knots. The first chapter is purely algebraic. The rest of
the book may be divided into three parts: general results on homotopy and
surgery (Chapters 2-6), geometries and geometric decompositions (Chapters
7-13), and 2-knots (Chapters 14-18). In many cases the Euler characteristic,
fundamental group and Stiefel-Whitney classes together form a complete system
of invariants for the homotopy type of such manifolds, and the possible values
of the invariants can be described explicitly. The strongest results are
characterizations of manifolds which fibre homotopically over S^1 or an
aspherical surface (up to homotopy equivalence) and infrasolvmanifolds (up to
homeomorphism). As a consequence 2-knots whose groups are poly-Z are determined
up to Gluck reconstruction and change of orientations by their groups alone.
This book arose out of two earlier books "2-Knots and their Groups" and "The
Algebraic Characterization of Geometric 4-Manifolds", published by Cambridge
University Press for the Australian Mathematical Society and for the London
Mathematical Society, respectively. About a quarter of the present text has
been taken from these books, and I thank Cambridge University Press for their
permission to use this material. The book has been revised in March 2007. For
details see the end of the preface.Comment: This is the revised version published by Geometry & Topology
Monographs in March 200