Title :
On several new projective curves over F2 of genus 3, 4, and 5
Author :
Moreno, Oscar ; Zinoviev, Dmitrii ; Zinoviev, Victor
Author_Institution :
Dept. of Math., Puerto Rico Univ., Rio Piedras, Puerto Rico
fDate :
11/1/1995 12:00:00 AM
Abstract :
Using known techniques of desingularization for singular plane projective curves over finite fields Fq, q=2m, we found several new binary plane projective curves of genus 3, 4, and 5 with the maximal number of Fq-rational points (q=2m, m=3, 4, 5, 6, 7, 8, and 9) on their smooth projective models, which are close to or meet Serre´s upper bound
Keywords :
Goppa codes; algebraic geometric codes; Fq-rational points; Goppa codes; Serre´s upper bound; algebraic-geometric codes; binary plane projective curves; desingularization; finite fields; genus; singular plane projective curves; smooth projective models; Algebra; Contracts; Galois fields; Information theory; Integral equations; Mathematics; Polynomials; Upper bound; Workstations;
Journal_Title :
Information Theory, IEEE Transactions on
