Computing the linear complexity for sequences with characteristic polynomial fv

Authors:
Ana Sälägean;Alex J. Burrage;Raphael C. Phan
Affiliations:
Department of Computer Science, Loughborough University, Loughborough, UK;Qualcomm, Farnborough, UK;Faculty of Engineering, Multimedia University, Cyberjaya, Malaysia
Venue:
Cryptography and Communications
Year:
2013

Citing 4
Cited 0

Introduction to finite fields and their applications

Introduction to finite fields and their applications
Shift Register Sequences

Shift Register Sequences
A fast algorithm for determining the complexity of a binary sequence with period (Corresp.)

IEEE Transactions on Information Theory
On the computation of the linear complexity and the k-error linear complexity of binary sequences with period a power of two

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present several generalisations of the Games---Chan algorithm. For a fixed monic irreducible polynomial f we consider the sequences s that have as a 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 Ding 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 proposed algorithms 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.