Pseudo-random sequences are a crucial component of cryptography, particularly
in stream cipher design. In this thesis we will investigate several measures of
randomness for certain classes of finitely generated sequences.
We will present a heuristic algorithm for calculating the k-error linear complexity
of a general sequence, of either finite or infinite length, and results on the
closeness of the approximation generated.
We will present an linear time algorithm for determining the linear complexity
of a sequence whose characteristic polynomial is a power of an irreducible element,
again presenting variations for both finite and infinite sequences. This algorithm
allows the linear complexity of such sequences to be determined faster than was
Finally we investigate the stability of m-sequences, in terms of both k-error
linear complexity and k-error period. We show that such sequences are inherently
stable, but show that some are more stable than others.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.