Nonexistence of certain binary orthogonal arrays

Nonexistence of a few binary orthogonal arrays

We develop and apply combinatorial algorithms for investigation of the feasible distance distributions of binary orthogonal arrays with respect to a point of the ambient binary Hamming space utilizing constraints imposed from the relations between the distance distributions of connected arrays. This turns out to be strong enough and we prove the nonexistence of binary orthogonal arrays of param...

Nonexistence of (9, 112, 4) and (10, 224, 5) binary orthogonal arrays

Nonexistence of ( 9 , 112 , 4 ) and ( 10 , 224 , 5 ) binary orthogonal arrays 1

Our approach is a natural continuation of the algorithm which is presented in [3]. We prove the nonexistence of BOAs of parameters (length, cardinality, strength) = (9, 7.2 = 112, 4) and (10, 7.2 = 224, 5), resolving two cases where the existence was undecided up to now.

On the existence of nested orthogonal arrays

A nested orthogonal array is an OA(N, k, s, g)which contains an OA(M, k, r, g) as a subarray. Here r < s andM<N . Necessary conditions for the existence of such arrays are obtained in the form of upper bounds on k, given N,M, s, r and g. Examples are given to show that these bounds are quite powerful in proving nonexistence. The link with incomplete orthogonal arrays is also indicated. © 2007 E...

On orthogonal polynomials for certain non-definite linear functionals

We consider the non-definite linear functionals Ln[f ] = ∫ IR w(x)f (n)(x) dx and prove the nonexistence of orthogonal polynomials, with all zeros real, in several cases. The proofs are based on the connection with moment preserving spline approximation.