Value sets of Dickson polynomials over Galois rings
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TLDR
In this article, the cardinality of the preimage of a Dickson polynomial over a Galois ring is determined. But the cardinalities of the value set of a preimage are not known.About:
This article is published in Journal of Number Theory.The article was published on 1991-06-01 and is currently open access. It has received 4 citations till now. The article focuses on the topics: Galois extension & Ring of integers.read more
Citations
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Dickson Polynomial Discriminators
Pieter Moree,Gary L. Mullen +1 more
TL;DR: In this paper, the Dickson discriminator problem was studied for finding the smallest positive integer k for which the integers g j (1, ǫ), g j(2,ǫ, a ), g n (n, n, a), g g(n, a ) are distinct modulo k for all integers a and all natural numbers j and n.
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Functions and polynomials over Galois rings
Joel V. Brawley,Gary L. Mullen +1 more
TL;DR: In this paper, the authors derive formulas for the total number of functions from R to itself which can be represented by polynomials over R and also derive a formula for the number of such permutations of R.
Journal ArticleDOI
Properties of Chebyshev Polynomials Modulo $p^k$
TL;DR: In this brief, the sequence period of Chebyshev polynomials modulo a prime power is obtained analytically and provides a design strategy for applications requiring a specific period.
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The value set of polynomials over ℤ m and the combinatorics of sequences
TL;DR: For a class of functions containing polynomials over Ω m, this article gave an inequality relating the cardinality of the value set to the additive order of differences of elements in that set.
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Value sets of Dickson polynomials over finite fields
TL;DR: In this article, the cardinality of the value set for the Dickson polynomial gd(x, a) over a finite field of order q where q is a prime power was determined.