TY - JOUR

T1 - The number of rational points on hyperelliptic supersingular curves of genus 4 in characteristic 2

AU - McGuire, Gary

AU - Zaytsev, Alexey

N1 - Funding Information:
E-mail addresses: gary.mcguire@ucd.ie (G. McGuire), alzaytsev@kantina.ru (A. Zaytsev). 1 Research supported by the Claude Shannon Institute, Science Foundation Ireland Grant 06/MI/006. 2 Research supported by Science Foundation Ireland Grant 07/RFP/MATF846.

PY - 2012/9

Y1 - 2012/9

N2 - One of the big questions in the area of curves over finite fields concerns the distribution of the numbers of points: which numbers occur as the number of points on a curve of genus g? The same question can be asked of various subclasses of curves. In this article we classify the possibilities for the number of points on hyperelliptic supersingular curves of genus 4 over finite fields of order 2 n, n odd.

AB - One of the big questions in the area of curves over finite fields concerns the distribution of the numbers of points: which numbers occur as the number of points on a curve of genus g? The same question can be asked of various subclasses of curves. In this article we classify the possibilities for the number of points on hyperelliptic supersingular curves of genus 4 over finite fields of order 2 n, n odd.

KW - 14H45

UR - http://www.scopus.com/inward/record.url?scp=84865660572&partnerID=8YFLogxK

U2 - 10.1016/j.ffa.2012.06.002

DO - 10.1016/j.ffa.2012.06.002

M3 - Article

AN - SCOPUS:84865660572

VL - 18

SP - 886

EP - 893

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

SN - 1071-5797

IS - 5

ER -