A099757 Molien series for complete weight enumerators of Hermitian self-dual codes over the Galois ring GR(4,2).

1, 1, 5, 5, 37, 55, 309, 551, 2203, 4244, 13162, 25440, 66070, 124994, 285536, 523098, 1085624, 1921844, 3702554, 6338324, 11505922, 19087926, 33001680, 53187842, 88283749, 138577771, 222176121, 340466203, 529761539, 794259297, 1203988645, 1769515717

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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.: (g(t) + t^59*g(t^-1)) / ((1-t)*(1-t^2)^4*(1-t^4)^6*(1-t^6)^3*(1-t^12)^2) where g(t) = 1 + 16*t^4 + 18*t^5 + 143*t^6 + 170*t^7 + 696*t^8 + 1073*t^9 + 2786*t^10 + 4420*t^11 + 8881*t^12 + 13782*t^13 + 23018*t^14 + 33979*t^15 + 50086*t^16 + 69748*t^17 + 94127*t^18 + 123476*t^19 + 155400*t^20 + 192999*t^21 + 229352*t^22 + 270342*t^23 + 306276*t^24 + 343736*t^25 + 372818*t^26 + 399845*t^27 + 415884*t^28 + 425872*t^29 [Nebe, Rains, Sloane, p. 241]. [Incorrect formula replaced by the correct one by Georg Fischer and Andrey Zabolotskiy, Jan 25 2021]

Crossrefs

Sequence in context: A269876 A139386 A074947 * A374652 A271091 A271289

Adjacent sequences: A099754 A099755 A099756 * A099758 A099759 A099760

Keyword

nonn

Author

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

Status

approved