New curves with many points over small finite fields
2013 (English)In: Finite Fields and Their Applications, ISSN 1071-5797, E-ISSN 1090-2465, Vol. 21, 58-66 p.Article in journal (Refereed) Published
We use class field theory to search for curves with many rational points over the finite fields of cardinality <= 5. By going through abelian covers of each curve of genus s <= 2 over these fields we find a number of new curves. In particular, over F-2 we settle the question of how many points there can be on a curve of genus 17 by. finding one with 18 points. The search is aided by computer; in some cases it is exhaustive for this type of curve of genus up to
Place, publisher, year, edition, pages
2013. Vol. 21, 58-66 p.
Curves, Rational points
IdentifiersURN: urn:nbn:se:su:diva-89573DOI: 10.1016/j.ffa.2013.01.007ISI: 000316034600006OAI: oai:DiVA.org:su-89573DiVA: diva2:618619