Journal ArticleDOI
When does a polynomial over a finite field permute the elements of the fields
Rudolf Lidl,Gary L. Mullen +1 more
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In this paper, when does a polynomial over a finite field permute the elements of the field? The American Mathematical Monthly: Vol 95, No 3, pp 243-246Abstract:
(1988) When Does a Polynomial over a Finite Field Permute the Elements of the Field? The American Mathematical Monthly: Vol 95, No 3, pp 243-246read more
Citations
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Journal ArticleDOI
Permutation polynomials and applications to coding theory
TL;DR: Applications in coding theory mainly related to a conjecture of Helleseth are given and an estimation of the number of permutation binomials of the form X^r(X^(^q^-^1^)^/^m+a) for a@?F"q^*.
Journal ArticleDOI
Soft-decision decoding of Reed-Muller codes: recursive lists
Ilya Dumer,Kirill Shabunov +1 more
TL;DR: Simulation results show that for all RM codes of length 256 and many subcodes of length 512, these algorithms approach maximum-likelihood (ML) performance within a margin of 0.1 dB.
Journal ArticleDOI
Permutation polynomials of the formx r f(x q?1)/d) and their group structure
Daqing Wan,Rudolf Lidl +1 more
TL;DR: In this paper, the authors give a systematic treatment of permutation polynomials (over a finite field) of the formx.............. r ¯¯ ¯¯ f (x¯¯¯¯¯¯¯¯q−1)/d, and prove that all such polynomial groups are isomorphic to a generalized wreath product of certain abelian groups.
Journal ArticleDOI
Permutation polynomials and group permutation polynomials
Young Ho Park,June Bok Lee +1 more
TL;DR: In this article, a group permutation polynomials of the form xτf (x3) over a finite field are defined and a group theoretic criterion and some other criteria in terms of symmetric functions and power functions are given.
Book ChapterDOI
Cyclotomic mapping permutation polynomials over finite fields
TL;DR: This work explores a connection between permutation polynomials of the form xrf(x(q-1)/l) and cyclotomic mapping permutation coefficients over finite fields and characterize a class of permutation binomials in terms of generalized Lucas sequences.
References
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MonographDOI
Introduction to finite fields and their applications
Rudolf Lidl,Harald Niederreiter +1 more
TL;DR: An introduction to the theory of finite fields, with emphasis on those aspects that are relevant for applications, especially information theory, algebraic coding theory and cryptology and a chapter on applications within mathematics, such as finite geometries.
Journal ArticleDOI
The Analytic Representation of Substitutions on a Power of a Prime Number of Letters with a Discussion of the Linear Group.
Journal ArticleDOI
Planes of order n with collineation groups of order n 2
Peter Dembowski,T. G. Ostrom +1 more