Beyond the orthogonal array concept

Consider a block code Γ of length n, over a q-ary alphabet. For a given integer t∈[0,n], the regularity of Γ at level t is measured by the dimension of a well-defined subspace F of Rt+1, called the t-form space of the code. In particular, Γ is an orthogonal array of strength t if and only if F=Rt+1. A central result of the paper is the close connection that exists between t-forms and T-designs in the Hamming scheme H(n,q). The t-form space F is shown to have the structure of an ideal, and the canonical generator of F to be computable from the distance distribution of the code Γ.