On pseudo-noise sequences

The discovery of pseudo-noise sequences is a product of coding theory -- an area of mathematics which deals with the transmission and reception of messages across noisy channels. To give a partial exposition of the article entitled Applications of Coding Theory in Mobile Radio Communications by Derek Smith and Stephanie Perkins [15] is the main aim of this thesis. Also, it aims to discuss in detail the properties of pseudo-noise sequences using the book entitled The Theory of Error-Correcting Codes by Florence MacWilliams and Neil Sloane [10]. In order to give a clear understanding of these properties, basic concepts in abstract algebra, linear algebra, field theory and coding theory are provided. The use of linear feedback shift registers for a fast generation of pseudo-noise sequences is also discussed. Ten properties are verified, and these include properties about pseud-randomness and autocorrelation. It is proven that a pseudo-noise sequence satisfies a certain recurrence and is periodic with period n = 2m - 1, where m is the degree of the primitive irreducible polynomial used for constructing a linear feedback shift register that there are 2m - 1 nonzero states before repeating that each possible nonzero m-tuple is seen only once in a full period of a pseudo-noise sequence and that the sum of any segment (of length n from a pseudo-noise sequence) with a cyclic shift of itself is another cyclic shift of this segment