A014116 Order of automorphism group of Barnes-Wall lattice in dimension 2^n.

2, 8, 1152, 696729600, 89181388800, 48126558103142400, 409825748158189771161600, 55428899652335313894424707072000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 129.

Links

• A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, Quantum error correction via codes over GF(4), arXiv:quant-ph/9608006, 1996-1997; IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.
• G. E. Wall, On the Clifford collineation, transform and similarity groups. IV. An application to quadratic forms, Nagoya Math. J., 21 (1962), pp. 199-222.
• Index entries for sequences related to Barnes-Wall lattices

Crossrefs

Agrees with A014115 except at n=3. Equals half of A001309. Cf. A003956.

Programs

Maple

2^(n^2+n+1) * (2^n - 1) * product('2^(2*i)-1','i'=1..n-1); # except for n=3.

Python

from math import prod
def A014116(n): return 2+696729598*(n//3) if n == 0 or n == 3 else ((1<Chai Wah Wu, Jun 20 2022