

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



CROSSREFS



KEYWORD

nonn


AUTHOR

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


STATUS

approved



