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A099757
Molien series for complete weight enumerators of Hermitian self-dual codes over the Galois ring GR(4,2).
0
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
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
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
KEYWORD
nonn
AUTHOR
G. Nebe (nebe(AT)math.rwth-aachen.de), Nov 10, 2004
STATUS
approved