Frequency permutation arrays

✍ Scribed by Sophie Huczynska; Gary L. Mullen

• Book ID: 102308164
• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 158 KB
• Volume: 14
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20096

✦ Synopsis

Abstract

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 = __m__λ 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. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 463–478, 2006