A058224 Largest d such that the linear programming bound for quantum codes of length n is feasible for some real K>1.

1, 1, 1, 2, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9, 10, 11, 11, 11, 11, 11, 12, 13, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 16, 17, 17, 17, 17, 17, 18, 19, 19, 19, 19, 19, 20, 21, 21, 21, 21, 21, 22, 23, 23, 23, 23, 23, 24, 25, 25, 25, 25, 25

Offset

1,4

Comments

Bounded above by floor((n+1)/6)+floor((n+2)/6)+1 for all n, with equality when n < 100. For n < 22 and 25 <= n <= 30 this bound is attained by actual additive quantum codes; for other values of n, this is unknown.

References

E. M. Rains, Shadow bounds for self-dual codes, IEEE Trans. Inform. Theory, 44 (No. 1, 1998), 134-139.

E. M. Rains, Monotonicity of the quantum linear programming bound, IEEE Trans. Inform. Theory, 45 (No. 7, 1999), 2489-2491.

Links

Table of n, a(n) for n=1..75.

Crossrefs

Sequence in context: A362960 A189635 A109785 * A131808 A196183 A200264

Adjacent sequences: A058221 A058222 A058223 * A058225 A058226 A058227

Keyword

nonn

Author

Eric M. Rains (rains(AT)caltech.edu), Dec 02 2000

Status

approved