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A169873
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Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 2 over the field F_2^n.
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1
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6, 10, 18, 33, 53, 97, 172, 321, 603, 1153, 2227, 4353, 8553, 16897, 33491, 66561, 132519, 264193, 527183, 1052673, 2102943, 4202497, 8400192, 16793601, 33577603, 67141633, 134264067, 268500993, 536963592, 1073872897, 2147669011, 4295229441, 8590305319, 17180393473, 34360479823
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OFFSET
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1,1
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REFERENCES
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J. W. P. Hirschfeld, Linear codes and algebraic curves, pp. 35-53 of F. C. Holroyd and R. J. Wilson, editors, Geometrical Combinatorics. Pitman, Boston, 1984.
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LINKS
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PROG
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(Sage)
def a(n):
if n==2: return 10
elif (n%2 == 0): return 2^n + 1 + 2^(n/2+2)
elif ((floor(2^(n/2+1))%2 == 0) or (2^n-1).is_square()
or (4*2^n-3).is_square() or (4*2^n-7).is_square()):
if (frac(2^(n/2+1)) > ((sqrt(5)-1)/2)): return 2^n + 2*floor(2^(n/2+1))
else: return 2^n + 2*floor(2^(n/2+1)) - 1
else: return 2^n + 1 + 2*floor(2^(n/2+1)) # Robin Visser, Oct 01 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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