By Harald Niederreiter
Ever because the seminal paintings of Goppa on algebraic-geometry codes, rational issues on algebraic curves over finite fields were a massive learn subject for algebraic geometers and coding theorists. the point of interest during this program of algebraic geometry to coding thought is on algebraic curves over finite fields with many rational issues (relative to the genus). lately, the authors chanced on one other vital software of such curves, particularly to the development of low-discrepancy sequences. those sequences are wanted for numerical tools in components as various as computational physics and mathematical finance. This has given extra impetus to the idea of, and the quest for, algebraic curves over finite fields with many rational issues. This e-book goals to sum up the theoretical paintings on algebraic curves over finite fields with many rational issues and to debate the functions of such curves to algebraic coding concept and the development of low-discrepancy sequences.
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