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A092203
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Molien series for 16-dimensional group of structure 2^4.O_{4}^{+}(F_2) = 2^4.(S_3 X S_3).2 and order 1152, corresponding to genus 2 complete weight enumerators of Hermitian self-dual GF(2)-linear codes over GF(4) containing the all-ones vector.
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1
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1, 1, 3, 7, 21, 47, 128, 303, 754, 1735, 3989, 8712, 18687, 38482, 77421, 150813, 286925, 531306, 962637, 1704506, 2959412, 5037606, 8426351, 13854300, 22426944, 35759968, 56234440, 87258555, 133730542, 202529129, 303328391, 449478982, 659401717, 958118335, 1379571974, 1969206260
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OFFSET
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0,3
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LINKS
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FORMULA
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For the Molien series see the Maple code.
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MAPLE
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f1:= 1 + t^3 + 5*t^4 + 18*t^5 + 45*t^6 + 88*t^7 + 196*t^8 + 394*t^9 + 804*t^10 + 1512*t^11 + 2702*t^12 + 4529*t^13 + 7218*t^14 + 11019*t^15 + 16064*t^16 + 22609*t ^17 + 30555*t^18 + 39889*t^19 + 50303*t^20 + 61476*t^21 + 72888*t^22 + 84047*t^23 + 94299*t^24 + 102995*t^25 + 109674*t^26 + 113791*t^27 + 57614*t^28;
f:= f1+expand(t^56*subs(t=1/t, f1));
g:= (1-t)*(1-t^2)^2*(1-t^3)^3*(1-t^4)^6*(1-t^6)*(1-t^8)^2*(1-t^12);
h:=f/g; # This is the Molien series
series(h, t, 48);
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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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There were errors in the definition (in the order and structure of the group). The rational form of the Molien series was correct, but the DATA section - the coefficients in the expansion of the Molien series - was wrong from the 28th term onwards. To make it easier to check I have replaced the formulas with Maple code based on the Latex source code for the book. Thanks to Georg Fischer and Andrey Zabolotskiy for noticing that something was wrong and proposing corrections. - N. J. A. Sloane, Jan 29 2021
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STATUS
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approved
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