Random Numbers. Sequences Based On Linear Feedback

Diploma Thesis, 2012

128 Pages, Grade: 2

Abstract or Introduction

7 is definately not a random number. In fact, we would probably say that the sequence 7, 2, 13, 9, 5, 8, ... is random. Within mathematics a sequence of random numbers should not display a pattern or show any form of regularity. Sequences of random numbers are generated by an algorithm that determines a succeeding number using one or more given
numbers. Numbers yielded by an algorithm are called pseudo-random numbers which can be denoted mathematically. Multidimensional equidistribution and a large period are important properties required from a sequence in order to acknowledge it as random numbers. The algorithms to produce random numbers can be roughly grouped into two families
- congruential generators and generators based on feedback shift registers (FSR). We will focus on the latter family. An FSR-based generator can be described by a characteristic
polynomial which has to be primitive in order to ensure the best quality with respect to randomness. Often sparse polynomials are used to reduce computing costs. The algorithms used produce random sequences that might have some deficiencies. However, the quality of randomness can be improved by several measurements; as are modifying the feedback, filtering the output sequences or combining two or more generators.


Random Numbers. Sequences Based On Linear Feedback
Klagenfurt University  (Institut für Statistik)
Catalog Number
ISBN (eBook)
ISBN (Book)
File size
5321 KB
random, numbers, random numbers, sequence, pattern, algorithm, pseudo-random numbers, equidistribution, period, feedback shift register, polynomial, characteristic polynomial, primitive, primitive polynomial, sparse polynomials, deficiency, modify feedback, filter, filter output, combine generators
Quote paper
Christian Mößlacher (Author), 2012, Random Numbers. Sequences Based On Linear Feedback, Munich, GRIN Verlag, https://www.grin.com/document/302951


  • No comments yet.
Read the ebook
Title: Random Numbers. Sequences Based On Linear Feedback

Upload papers

Your term paper / thesis:

- Publication as eBook and book
- High royalties for the sales
- Completely free - with ISBN
- It only takes five minutes
- Every paper finds readers

Publish now - it's free