cp's OEIS Frontend

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

%I A099720 #8 Jul 01 2025 15:58:15
%S A099720 1,1,1,3,9,9,19,45,145,260,604,1354,3182,6298,13020,25642,50388,92820,
%T A099720 170578,303424,533798,908606,1530476,2522074,4107717,6553695,10343897,
%U A099720 16070605,24706363,37437245,56184469,83316627,122439255,177978716,256574818,366404272
%N A099720 Molien series for complete weight enumerators of Euclidean self-dual codes over the Galois ring GR(4,2).
%H A099720 G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.
%H A099720 <a href="/index/Mo#Molien">Index entries for Molien series</a>
%F A099720 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 A099720 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 +
%F A099720 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.
%K A099720 nonn
%O A099720 0,4
%A A099720 G. Nebe (nebe(AT)math.rwth-aachen.de), Nov 10 2004