A099720 Molien series for complete weight enumerators of Euclidean self-dual codes over the Galois ring GR(4,2).

1, 1, 1, 3, 9, 9, 19, 45, 145, 260, 604, 1354, 3182, 6298, 13020, 25642, 50388, 92820, 170578, 303424, 533798, 908606, 1530476, 2522074, 4107717, 6553695, 10343897, 16070605, 24706363, 37437245, 56184469, 83316627, 122439255, 177978716, 256574818, 366404272

Offset: 0

Author

G. Nebe (nebe(AT)math.rwth-aachen.de), Nov 10 2004

Keywords

• nonn

Links

• G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
• Index entries for Molien series

Formula

G.f.: u1/u2 where u1 := f(t) + t^72*f(t^-1), u2 := (1-t)*(1-t^3)*(1-t^4)^5*(1-t^6)^4*(1-t^8)^5 and

f(t) = 1+t^3 + t^4 + 4*t^6 + 15*t^7 + 75*t^8 + 101*t^9 + 274*t^10 + 555*t^11 + 1232*t^12 +2187*t^13 + 4122*t^14 + 7245*t^15 + 12514*t^16 + 20155*t^17 + 31998*t^18 + 48747*t^19 + 72408*t^20 + 103925*t^21 +

144878*t^22 + 197573*t^23 + 261102*t^24 + 338155*t^25 + 425254*t^26 + 524445*t^27 + 629888*t^28 + 740973*t^29 + 851614*t^30 + 957155*t^31 + 1053412*t^32 + 1133809*t^33 + 1196064*t^34 + 1233375*t^35 + 1247150/2*t^36.