36,260 research outputs found
Minimal Polynomial Algorithms for Finite Sequences
We show that a straightforward rewrite of a known minimal polynomial
algorithm yields a simpler version of a recent algorithm of A. Salagean.Comment: Section 2 added, remarks and references expanded. To appear in IEEE
Transactions on Information Theory
Linear complexity for sequences with characteristic polynomial fv
We present several generalisations of the Games-
Chan algorithm. For a fixed monic irreducible polynomial f we
consider the sequences s that have as characteristic polynomial
a power of f. We propose an algorithm for computing the linear
complexity of s given a full (not necessarily minimal) period of
s. We give versions of the algorithm for fields of characteristic 2
and for arbitrary finite characteristic p, the latter generalising an
algorithm of Kaida et al. We also propose an algorithm which
computes the linear complexity given only a finite portion of
s (of length greater than or equal to the linear complexity),
generalising an algorithm of Meidl. All our algorithms have
linear computational complexity. The algorithms for computing
the linear complexity when a full period is known can be further
generalised to sequences for which it is known a priori that the
irreducible factors of the minimal polynomial belong to a given
small set of polynomials
On the calculation of the linear complexity of periodic sequences
Based on a result of Hao Chen in 2006 we present a general procedure how to reduce the determination of the linear complexity of a sequence over a finite field \F_q of period to the determination of the linear complexities of sequences over \F_q of period . We apply this procedure to some classes of
periodic sequences over a finite field \F_q obtaining efficient algorithms to determine the linear complexity
How to determine linear complexity and -error linear complexity in some classes of linear recurring sequences
Several fast algorithms for the determination of the linear complexity of -periodic sequences over a finite
field \F_q, i.e. sequences with characteristic polynomial , have been proposed in the literature.
In this contribution fast algorithms for determining the linear complexity of binary sequences with characteristic
polynomial for an arbitrary positive integer , and are presented.
The result is then utilized to establish a fast algorithm for determining the -error linear complexity of
binary sequences with characteristic polynomial
Tractability of multivariate analytic problems
In the theory of tractability of multivariate problems one usually studies
problems with finite smoothness. Then we want to know which -variate
problems can be approximated to within by using, say,
polynomially many in and function values or arbitrary
linear functionals.
There is a recent stream of work for multivariate analytic problems for which
we want to answer the usual tractability questions with
replaced by . In this vein of research, multivariate
integration and approximation have been studied over Korobov spaces with
exponentially fast decaying Fourier coefficients. This is work of J. Dick, G.
Larcher, and the authors. There is a natural need to analyze more general
analytic problems defined over more general spaces and obtain tractability
results in terms of and .
The goal of this paper is to survey the existing results, present some new
results, and propose further questions for the study of tractability of
multivariate analytic questions
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