Nonexistence of a few 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 certain binary orthogonal arrays

We prove that binary orthogonal arrays of strength 8, length 12 and cardinality 1536 do not exist. This implies the nonexistence of arrays of parameters (strength,length,cardinality) = (n, n + 4, 6.2) for every integer n ≥ 8.

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.

Enumeration of binary orthogonal arrays of strength 1

A k2m×n (0,1) matrix is called a binary orthogonal array of strength m if in any m columns of the matrix every one of the possible 2 ordered (0,1) m-tuples occurs in exactly k rows and no two rows are identical. In this paper, the enumeration of binary orthogonal arrays is studied, and a closed expression for the enumeration of binary orthogonal arrays of strength 1 is given using the inclusion...