

A058224


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


0



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
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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 selfdual codes, IEEE Trans. Inform. Theory, 44 (No. 1, 1998), 134139.
E. M. Rains, Monotonicity of the quantum linear programming bound, IEEE Trans. Inform. Theory, 45 (No. 7, 1999), 24892491.


LINKS

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


CROSSREFS

Sequence in context: A068953 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



