2,919 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
On the failure of pseudo-nullity of Iwasawa modules
We consider the family of CM-fields which are pro-p p-adic Lie extensions of
number fields of dimension at least two, which contain the cyclotomic
Z_p-extension, and which are ramified at only finitely many primes. We show
that the Galois groups of the maximal unramified abelian pro-p extensions of
these fields are not always pseudo-null as Iwasawa modules for the Iwasawa
algebras of the given p-adic Lie groups. The proof uses Kida's formula for the
growth of lambda-invariants in cyclotomic Z_p-extensions of CM-fields. In fact,
we give a new proof of Kida's formula which includes a slight weakening of the
usual assumption that mu is trivial. This proof uses certain exact sequences
involving Iwasawa modules in procyclic extensions. These sequences are derived
in an appendix by the second author.Comment: 26 page
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
The representation type of Ariki-Koike algebras and cyclotomic q-Schur algebras
We give a necessary and sufficient condition on parameters for Ariki-Koike
algebras (resp. cyclotomic q-Schur algebras) to be of finite representation
type.Comment: 23 pages, revised version (correcting some errors, containing some
extended results), to appear in Adv. Mat
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