{"id":{"repo_id":"siu-theses","oai_identifier":"oai:opensiuc.lib.siu.edu:dissertations-1910"},"canonical_url":"https://search.dev.ndltd.org/etd/siu-theses/oai:opensiuc.lib.siu.edu:dissertations-1910","repository":{"repo_id":"siu-theses","name":"Southern Illinois University","base_url":"https://opensiuc.lib.siu.edu/do/oai/"},"display":{"title":"The number of zeros of linear recurring sequences over finite fields","abstract":"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 q elements, based on an irreducible minimal polynomials of degree d and order m 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 t= (qd-1)/m has the form qa+1 or q2a-qa+1 where a 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.","abstract_html":"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.","abstract_has_math":false,"creators":["Kottegoda, Suwanda Hennedige Yasanthi"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Campus Only Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Fitzgerald, Robert"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-08-01T07:00:00Z","date_published":"2014-08-01T07:00:00Z","updated_at":"2026-07-24T04:34:30Z","subjects":["finite fields","linear recurring sequences"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opensiuc.lib.siu.edu/dissertations/907","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Fitzgerald, Robert"]},{"key":"dc:creator","label":"Author","values":["Kottegoda, Suwanda Hennedige Yasanthi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Only Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["finite fields","linear recurring sequences"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://opensiuc.lib.siu.edu/dissertations/907"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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 q elements, based on an irreducible minimal polynomials of degree d and order m 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 t= (qd-1)/m has the form qa+1 or q2a-qa+1 where a 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."]},{"key":"dc:title","label":"Title","values":["The number of zeros of linear recurring sequences over finite fields"]}]}],"canonical_facts":{"dc:contributor":["Fitzgerald, Robert"],"dc:creator":["Kottegoda, Suwanda Hennedige Yasanthi"],"dc:description.abstract":["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 q elements, based on an irreducible minimal polynomials of degree d and order m 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 t= (qd-1)/m has the form qa+1 or q2a-qa+1 where a 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."],"dc:identifier":["https://opensiuc.lib.siu.edu/dissertations/907"],"dc:subject":["finite fields","linear recurring sequences"],"dc:title":["The number of zeros of linear recurring sequences over finite fields"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Campus Only Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T04:34:30Z"}