The number of zeros of linear recurring sequences over finite fields

In this dissertation, I discuss bounds for the set of possible number of zeros of a homogeneous linear recurring sequence over a finite field of <italic>q<italic> elements, based on an irreducible minimal polynomials of degree <italic>d<italic> and order <italic>m<italic> as the characteristic polynomial. I prove upper and lower bounds on the cardinality of the set of number of zeros. The set is determined when <italic>t= (q<super>d<super>-1)/m<italic> has the form <italic>q<super>a<super>+1<italic> or <italic>q<super>2a<super>-q<super>a<super>+1<italic> where <italic>a<italic> is a positive integer. The connection with coding theory is a key ingredient. Also it is proved that the upper bound defined here is the best bound for the cardinality of the set of zeros, in the sense that it is reached infinitely often.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Campus Only Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2014

Author dc:creator

• Kottegoda, Suwanda Hennedige Yasanthi

Contributors dc:contributor

• Fitzgerald, Robert

• finite fields
• linear recurring sequences

Repository record dc:identifier

https://opensiuc.lib.siu.edu/dissertations/907

OAI identifier oai:identifier

oai:opensiuc.lib.siu.edu:dissertations-1910