▁exists ▁a ▁ 2 -( 2 , ▁ 4 m   −   1 , ▁m ) ▁orthogonal ▁array . ▁ ▁Let ▁H ▁be ▁a ▁Had am ard ▁matrix ▁of ▁order ▁ 4 m ▁in ▁standard ized ▁form ▁( first ▁row ▁and ▁column ▁entries ▁are ▁all ▁+ 1 ). ▁Delete ▁the ▁first ▁row ▁and ▁take ▁the ▁trans pose ▁to ▁obtain ▁the ▁desired ▁orthogonal ▁array . ▁ ▁The ▁order ▁ 8 ▁standard ized ▁Had am ard ▁matrix ▁below ▁( ± 1 ▁entries ▁indicated ▁only ▁by ▁sign ), ▁ ▁produces ▁the ▁ 2 -( 2 , 7 , 2 ) ▁orthogonal ▁array : ▁ ▁Using ▁columns ▁ 1 , ▁ 2 ▁and ▁ 4 ▁as ▁indexing ▁columns , ▁the ▁remaining ▁columns ▁produce ▁four ▁mut ually ▁orthogonal ▁latin ▁cub es ▁of ▁order ▁ 2 . ▁ ▁C odes ▁ ▁Let ▁C ▁ ⊆ ▁( F q ) n , ▁be ▁a ▁linear ▁code ▁of ▁dimension ▁m ▁with ▁minimum ▁distance ▁d . ▁Then ▁C ⊥ ▁( the ▁orthogonal ▁complement ▁of ▁the ▁vector ▁sub space ▁C ) ▁is ▁a ▁( linear ) ▁( d   −   1 )- ( q , ▁n , ▁ λ ) ▁orthogonal ▁array ▁where ▁▁ λ   =   q n   −   m   −   d   +   1 . ▁ ▁App lications ▁ ▁Th reshold ▁schemes ▁ ▁Secret ▁sharing ▁( also ▁called ▁secret ▁splitting ) ▁consists ▁of ▁methods ▁for ▁distrib uting ▁a ▁secret ▁amongst ▁a ▁group ▁of ▁participants , ▁each ▁of ▁whom ▁is ▁allocated ▁a ▁share ▁of