Recursive constructions for equidistant permutation arrays

Abstract

AbstractAn equidistant permutation array (EPA) is a ν ×rarray defined on anr-set,R, such that (i) each row is a permutation of the elements ofRand (ii) any two distinct rows agree in λ positions (that is, the Hamming distance is (r−λ)).Such an array is said to have order ν. In this paper we give several recursive constructions for EPA's.The first construction uses a resolvable regular pairwise balanced design of ordervto construct an EPA of order ν. The second construction is a generalization of the direct product construction for Room squares.We also give a construction for intersection permutation arrays, which arrays are a generalization of EPA's.