Global Function Fields With Many Rational Places Over the Quinary Field

Niederreiter, Harald; Xing, Chaoping

doi:10.1515/dema-1997-0421

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Implementation and Results1

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1998

2012

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Cited by 7 publications

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“…Curves over F 5 . For q = 5 there had been some previous work, e.g., [8], [9] and [10], in particular using the present method. By doing the systematic search we found 3 improvements of the old table entries:…”

Section: Implementation and Resultsmentioning

confidence: 87%

Computer search for curves with many points among abelian covers of genus 2 curves

Rökaeus¹

2012

Contemporary Mathematics

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1 Using class field theory one associates to each curve C over a finite field, and each subgroup G of its divisor class group, unramified abelian covers of C whose genus is determined by the index of G. By listing class groups of curves of small genus one may get examples of curves with many points; we do this for all curves of genus 2 over the fields of cardinality 5,7,9,11,13 and 16, giving new entries for the tables of curves with many points [6].

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Section: Implementation and Resultsmentioning

confidence: 87%