10,201 research outputs found
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=m lambda and distance d is a set T of multipermutations on a
multiset of m symbols, each repeated with frequency lambda, such that the
Hamming distance between any distinct x,y in T is at least d. Such arrays have
potential applications in powerline communication. In this paper, 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.Comment: To appear in Journal of Combinatorial Design
A Recursive Construction of Permutation Polynomials over with Odd Characteristic from R\'{e}dei Functions
In this paper, we construct two classes of permutation polynomials over
with odd characteristic from rational R\'{e}dei functions. A
complete characterization of their compositional inverses is also given. These
permutation polynomials can be generated recursively. As a consequence, we can
generate recursively permutation polynomials with arbitrary number of terms.
More importantly, the conditions of these polynomials being permutations are
very easy to characterize. For wide applications in practice, several classes
of permutation binomials and trinomials are given. With the help of a computer,
we find that the number of permutation polynomials of these types is very
large
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