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On several new projective curves over F2 of genus 3, 4, and 5

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3 Author(s)
Moreno, O. ; Dept. of Math., Puerto Rico Univ., Rio Piedras, Puerto Rico ; Zinoviev, D. ; Zinoviev, V.

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

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Information Theory, IEEE Transactions on  (Volume:41 ,  Issue: 6 )