Permutation polynomials and applications to coding theory

AbstractWe present different results derived from a theorem stated by Wan and Lidl [Permutation polynomials of the form xrf(x(q-1)/d) and their group structure, Monatsh. Math. 112(2) (1991) 149–163] which treats specific permutations on finite fields. We first exhibit a new class of permutation binomials and look at some interesting subclasses. We then give an estimation of the number of permutation binomials of the form Xr(X(q-1)/m+a) for a∈Fq*. Finally we give applications in coding theory mainly related to a conjecture of Helleseth

Some Proposed Problems on Permutation Polynomials over Finite Fields

From the 19th century, the theory of permutation polynomial over finite fields, that are arose in the work of Hermite and Dickson, has drawn general attention. Permutation polynomials over finite fields are an active area of research due to their rising applications in mathematics and engineering. The last three decades has seen rapid progress on the research on permutation polynomials due to their diverse applications in cryptography, coding theory, finite geometry, combinatorics and many more areas of mathematics and engineering. For this reason, the study of permutation polynomials is important nowadays. In this chapter, we propose some new problems in connection to permutation polynomials over finite fields by the help of prime numbers

Local permutation polynomials and the action of e-Klenian groups

Permutation polynomials of finite fields have many applications in Coding Theory, Cryptography and Combinatorics. In the first part of this paper we present a new family of local permutation polynomials based on a class of symmetric subgroups without fixed points, the so called e-Klenian groups. In the second part we use the fact that bivariate local permutation polynomials define Latin Squares, to discuss several constructions of Mutually Orthogonal Latin Squares (MOLS) and, in particular, we provide a new family of MOLS on size a prime power

On Maximum Contention-Free Interleavers and Permutation Polynomials over Integer Rings

An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Contention-free interleavers have been recently shown to be suitable for parallel decoding of turbo codes. In this correspondence, it is shown that permutation polynomials generate maximum contention-free interleavers, i.e., every factor of the interleaver length becomes a possible degree of parallel processing of the decoder. Further, it is shown by computer simulations that turbo codes using these interleavers perform very well for the 3rd Generation Partnership Project (3GPP) standard.Comment: 13 pages, 2 figures, submitted as a correspondence to the IEEE Transactions on Information Theory, revised versio