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A058224 Largest d such that the linear programming bound for quantum codes of length n is feasible for some real K>1. 0

%I #4 Dec 09 2007 03:00:00

%S 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,

%T 11,12,13,13,13,13,13,14,15,15,15,15,15,16,17,17,17,17,17,18,19,19,19,

%U 19,19,20,21,21,21,21,21,22,23,23,23,23,23,24,25,25,25,25,25

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

%C 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.

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

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

%K nonn

%O 1,4

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

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