Functions and polynomials over Galois rings

Joel V. Brawley; Gary L. Mullen

doi:10.1016/0022-314X(92)90116-7

Functions and polynomials over Galois rings

Joel V. Brawley, Gary L. Mullen

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Let R = GR(pⁿ, m) denote the Galois ring of order p^nm where p is a prime and n, m ≥ 1 are integers. 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 they also derive a formula for the number of such permutations of R. These results not only generalize but unify into a single theory, known results for finite fields and the integers mod pⁿ.

Original language	English (US)
Pages (from-to)	156-166
Number of pages	11
Journal	Journal of Number Theory
Volume	41
Issue number	2
DOIs	https://doi.org/10.1016/0022-314X(92)90116-7
State	Published - Jun 1992

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/0022-314X(92)90116-7

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title = "Functions and polynomials over Galois rings",

abstract = "Let R = GR(pn, m) denote the Galois ring of order pnm where p is a prime and n, m ≥ 1 are integers. 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 they also derive a formula for the number of such permutations of R. These results not only generalize but unify into a single theory, known results for finite fields and the integers mod pn.",

author = "Brawley, {Joel V.} and Mullen, {Gary L.}",

note = "Funding Information: author thanks the National Security Agency for partial support under grant MDA904-87-H-2023. The same author also thanks the Mathematical Sciences at Clemson University for its hospitality during his sabbatical when this paper",

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T1 - Functions and polynomials over Galois rings

AU - Brawley, Joel V.

AU - Mullen, Gary L.

N1 - Funding Information: author thanks the National Security Agency for partial support under grant MDA904-87-H-2023. The same author also thanks the Mathematical Sciences at Clemson University for its hospitality during his sabbatical when this paper

PY - 1992/6

Y1 - 1992/6

N2 - Let R = GR(pn, m) denote the Galois ring of order pnm where p is a prime and n, m ≥ 1 are integers. 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 they also derive a formula for the number of such permutations of R. These results not only generalize but unify into a single theory, known results for finite fields and the integers mod pn.

AB - Let R = GR(pn, m) denote the Galois ring of order pnm where p is a prime and n, m ≥ 1 are integers. 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 they also derive a formula for the number of such permutations of R. These results not only generalize but unify into a single theory, known results for finite fields and the integers mod pn.

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DO - 10.1016/0022-314X(92)90116-7

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VL - 41

SP - 156

EP - 166

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 2

ER -

Functions and polynomials over Galois rings

Abstract

All Science Journal Classification (ASJC) codes

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