A100025 Molien series for complete weight enumerators of trace-additive Hermitian self-dual codes over the Galois ring GR(4,2) that contain the all-ones vector.

1, 1, 7, 21, 92, 291, 981, 2871, 8134, 21131, 52481, 122759, 275356, 590289, 1220811, 2436045, 4715827, 8866230, 16246890, 29054190, 50830264, 87104226, 146467614, 241934106, 393098860, 628867434, 991602894, 1542350194, 2368492984, 3593354974

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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^41*f(1/t), u2 := (1-t)*(1-t^2)^6*(1-t^4)^7*(1-t^8)^2 and

f(t) := 1 + 14*t^3 + 43*t^4 + 115*t^5 + 334*t^6 + 808*t^7 + 1752*t^8 + 3557*t^9 + 6448*t^10 + 10800*t^11 + 17020*t^12 + 24972*t^13 + 34704*t^14 + 45824*t^15 + 57298*t^16 + 68464*t^17 + 78120*t^18 + 85092*t^19 + 88922*t^20.

Maple

f := 1 + 14*t^3 + 43*t^4 + 115*t^5 + 334*t^6 + 808*t^7 + 1752*t^8 + 3557*t^9 + 6448*t^10 + 10800*t^11 + 17020*t^12 + 24972*t^13 + 34704*t^14 + 45824*t^15 + 57298*t^16 + 68464*t^17 + 78120*t^18 + 85092*t^19 + 88922*t^20;
u1 := f + t^41*subs(t=1/t, f); u2 := (1-t)*(1-t^2)^6*(1-t^4)^7*(1-t^8)^2;
seq(coeff(series(u1/u2, t, n+1), t, n), n = 0..45); # Georg Fischer, Jan 25 2021

Crossrefs

Sequence in context: A114902 A177369 A164544 * A121157 A347863 A253072

Adjacent sequences: A100022 A100023 A100024 * A100026 A100027 A100028

Keyword

nonn

Author

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

Status

approved