By Harald Niederreiter

Ever because the seminal paintings of Goppa on algebraic-geometry codes, rational issues on algebraic curves over finite fields were a big learn subject for algebraic geometers and coding theorists. the point of interest during this software of algebraic geometry to coding thought is on algebraic curves over finite fields with many rational issues (relative to the genus). lately, the authors found one other vital program of such curves, particularly to the development of low-discrepancy sequences. those sequences are wanted for numerical equipment in parts as varied as computational physics and mathematical finance. This has given extra impetus to the idea of, and the hunt 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 purposes of such curves to algebraic coding thought and the development of low-discrepancy sequences.

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