Frequency permutation arrays

Motivated by recent interest in permutation arrays, we introduce and investigate the more general concept of frequency permutation arrays (FPAs). An FPA of length n - mX and distance d is a set T of multipermutations on a multiset of m symbols, each repeated with frequency λ, such that the Hamming distance between any distinct x,y ∈ T is at least d. Such arrays have potential applications in powerline communication. In this article, we establish basic properties of FPAs, and provide direct constructions for FPAs using a range of combinatorial objects, including polynomials over finite fields, combinatorial designs, and codes. We also provide recursive constructions, and give bounds for the maximum size of such arrays.