A003956 Order of complex Clifford group of degree 2^n arising in quantum coding theory.

8, 192, 92160, 743178240, 97029351014400, 203286581427673497600, 6819500449352277792129024000, 3660967964237442812098963052691456000, 31446995505814020383166371418359014222725120000

Offset

0,1

Links

T. D. Noe, Table of n, a(n) for n = 0..20

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. Nebe, E. M. Rains and N. J. A. Sloane, The invariants of the Clifford groups, arXiv:math/0001038 [math.CO], 2000; Des. Codes Crypt. 24 (2001), 99-121.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Edwin Pednault, An alternative approach to optimal wire cutting without ancilla qubits, arXiv:2303.08287 [quant-ph], 2023.

Tefjol Pllaha, Olav Tirkkonen, and Robert Calderbank, Binary Subspace Chirps, arXiv:2102.12384 [cs.IT], 2021.

B. Runge, Codes and Siegel modular forms, Discrete Math. 148 (1996), 175-204.

Index entries for sequences related to groups

Maple

a(n):= 2^(n^2+2*n+3)*mul(4^j-1, j=1..n); seq(a(n), n=0..10); # modified by G. C. Greubel, Sep 24 2019

Mathematica

Table[2^(n^2+2n+3) Product[4^j-1, {j, n}], {n, 0, 10}] (* Harvey P. Dale, Nov 03 2017 *)

Prog

(PARI) vector(11, n, 2^(n^2 +2)*prod(j=1, n-1, 4^j-1) ) \\ G. C. Greubel, Sep 24 2019
(Magma) [n eq 0 select 8 else 2^((n+1)^2+2)*(&*[4^j-1: j in [1..n]]): n in [0..10]]; // G. C. Greubel, Sep 24 2019
(Sage) [2^((n+1)^2 +2)*product(4^j -1 for j in (1..n)) for n in (0..10)] # G. C. Greubel, Sep 24 2019
(GAP) List([0..10], n-> 2^((n+1)^2 +2)*Product([1..n], j-> 4^j -1) ); # G. C. Greubel, Sep 24 2019
(Python)
from math import prod
def A003956(n): return prod((1<<i)-1 for i in range(2, 2*n+1, 2)) << n*(n+2)+3 # Chai Wah Wu, Jun 20 2022

Crossrefs

Cf. A001309, A014116, A014115, A027672.

Equals twice A027638.

Sequence in context: A071303 A128406 A265269 * A204820 A041269 A172340

Adjacent sequences: A003953 A003954 A003955 * A003957 A003958 A003959

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Peter Shor

Status

approved