A099748 Molien series for complete weight enumerators of Euclidean self-dual codes over the Galois ring GR(4,2) that contain the all-ones vector.

1, 2, 21, 225, 3328, 33518, 257909, 1544907, 7657779, 32454761, 121100938, 405911691, 1242567609, 3517715389, 9305703095, 23194232130, 54848107788, 123760738779, 267768667311, 557808040826, 1122804257019, 2190539008704, 4153269969884, 7670791137960

Offset

0,2

Links

Table of n, a(n) for n=0..23.

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^4) + t^156*f(t^-4), u2 := (1-t^4)^2*(1-t^8)^5*(1-t^12)^5*(1-t^16)^4 and

f(t) = 1 + 13*t^2 + 180*t^3 + 2815*t^4 + 26097*t^5 + 178909*t^6 + 914207*t^7 + 3741734*t^8 + 12638167*t^9 + 36300248*t^10 + 90284593*t^11 + 197531731*t^12 + 384302984*t^13 + 670899605*t^14 +

1057839714*t^15 + 1514398168*t^16 + 1975782327*t^17 + 2355691682*t^18 + 2571102793*t^19.

Crossrefs

Sequence in context: A106412 A329497 A058476 * A023812 A062813 A024231

Adjacent sequences: A099745 A099746 A099747 * A099749 A099750 A099751

Keyword

nonn

Author

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

Status

approved