Bounds and constructions for TWOOAs Original Research Article

A TWOOA is a pair of orthogonal arrays which satisfy a certain condition. Obana and Kurosawa introduced the notion of TWOOAs to construct multi-receiver authentication codes. In this paper, the upper bounds on n and m of a TWOOA(k,t2,n;2,tk,m) are determined to be mainly n⩽t+k−1 and m⩽t+1 by using the known Bush bound on orthogonal arrays. For a prime power q, a direct construction for a TWOOA(k,q2,m(k,q); 2,qk,q+1) is presented, where m(k,q) denotes the maximum number of vectors in Vk(GF(q)) such that any k of them are linearly independent. With the known results on m(k,q), this construction gives infinite classes of TWOOAs meeting the upper bounds. A product construction for TWOOAs is also given.