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Title: Global function fields with many rational places
Keywords: function fields, algebraic curves, rational places
Issue Date: 6-Feb-2004
Citation: TEO KAI MENG (2004-02-06). Global function fields with many rational places. ScholarBank@NUS Repository.
Abstract: We construct global function fields with many rational places based on Hilbert class fields defined over the finite field Fq for q = 3, 5, 7, 9, 25 and 49. With the help of Mathematica, a systematic sieve is performed on the set of all potentially good defining polynomials over Fq to obtain those that define global function fields with their number of rational places close to the theoretical upper bounds. These explicit polynomials are essential for practical applications in areas such as algebraic codes and low-discrepancy sequences. Several improvements have been made to the present records and many new results with high genera have been realized. As a prerequisite, a survey of the theory of algebraic function fields is also conducted.
Appears in Collections:Master's Theses (Open)

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