Slovak University of Technology, Bratislava

Faculty of Electrical Engineering and Information Technology

Degree Course: INFORMATICS

Author: Bc. Peter Šterbák

Diploma thesis: Distribution of Weight and Sphere Complexity and Period of Linear Recurring Sequences

Supervisor: RNDr. Karol Nemoga, PhD.

2002, December

Sequences in finite fields whose terms depend in simple manner on their predecessors are important for a variety of applications. Such sequences are easy to generate by recursive procedures and are called linear recurring sequences. Nowadays, there are securing information methods that concern with the theory of linear recurring sequences.

This project concerns with analysis, implementation and results of the calculations of linear recurring sequences, especially linear, weight, and sphere complexity of these sequences and their interdependencies.

The most significant theoretical facts dealing with linear recurring sequences are described, especially ones that are dealing with linear, weight, sphere complexity and are important in calculation of these parameters. Then there is description of implementation and results of system to various distributions of weight and sphere complexity and to finding for input sequence approximate sequence with smaller linear complexity. These computations were done for purpose of finding interdependencies of linear and sphere (weight) complexity, and also eventually showing importance of weight and sphere complexity of these sequences.