| Abstract |
For nonnegative integers n , d , and w , let A(n,d,w) be the maximum size of a code C⊆Fn2 with a constant weight w and minimum distance at least d . We consider two semidefinite programs based on quadruples of code words that yield several new upper bounds on A(n,d,w) . The new upper bounds imply that A(22,8,10)=616 and A(22,8,11)=672 . Lower bounds on A(22,8,10) and A(22,8,11) are obtained from the (n,d)=(22,7) shortened Golay code of size 2048. It can be concluded that the shortened Golay code is a union of constant-weight w codes of sizes A(22,8,w) .
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