Polynomials over base 2 finite fields with evenly distributed values

Thomas W. Cusick

doi:10.1016/j.ffa.2004.10.001

Polynomials over base 2 finite fields with evenly distributed values

Thomas W. Cusick

Mathematics

University at Buffalo

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

1 Scopus citations

Abstract

Few nontrivial results about the value sets of polynomials over finite fields are known. This paper uses results from the theory of crosscorrelation of binary m - sequences to find five kinds of polynomials f(x) defined over finite fields GF (2ⁿ) such that f(x) takes on each nonzero value only small a number of times (at most six times).

Original language	English
Pages (from-to)	278-291
Number of pages	14
Journal	Finite Fields and their Applications
Volume	11
Issue number	2
DOIs	https://doi.org/10.1016/j.ffa.2004.10.001
State	Published - Apr 2005

Keywords

Crosscorrelation
Finite fields
Value sets
m-sequences

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10.1016/j.ffa.2004.10.001

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title = "Polynomials over base 2 finite fields with evenly distributed values",

abstract = "Few nontrivial results about the value sets of polynomials over finite fields are known. This paper uses results from the theory of crosscorrelation of binary m - sequences to find five kinds of polynomials f(x) defined over finite fields GF (2n) such that f(x) takes on each nonzero value only small a number of times (at most six times).",

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T1 - Polynomials over base 2 finite fields with evenly distributed values

AU - Cusick, Thomas W.

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N2 - Few nontrivial results about the value sets of polynomials over finite fields are known. This paper uses results from the theory of crosscorrelation of binary m - sequences to find five kinds of polynomials f(x) defined over finite fields GF (2n) such that f(x) takes on each nonzero value only small a number of times (at most six times).

AB - Few nontrivial results about the value sets of polynomials over finite fields are known. This paper uses results from the theory of crosscorrelation of binary m - sequences to find five kinds of polynomials f(x) defined over finite fields GF (2n) such that f(x) takes on each nonzero value only small a number of times (at most six times).

KW - Crosscorrelation

KW - Finite fields

KW - Value sets

KW - m-sequences

UR - https://www.scopus.com/pages/publications/15544387443

U2 - 10.1016/j.ffa.2004.10.001

DO - 10.1016/j.ffa.2004.10.001

M3 - Article

SN - 1071-5797

VL - 11

SP - 278

EP - 291

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

IS - 2

ER -

Polynomials over base 2 finite fields with evenly distributed values

Abstract

Keywords

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