Value sets of some polynomials over finite fields GF(22m)

Thomas W. Cusick

doi:10.1137/S0097539794270352

Value sets of some polynomials over finite fields GF(2^2m)

Thomas W. Cusick

Mathematics

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

6 Scopus citations

Abstract

This paper shows that there is a connection between the crosscorrelation functions of certain binary m-sequences and the value sets of the polynomials x^k(1 + x)^2m-1 for k ∈ {±1, ±2,4}, where x is in the finite field GF(2^2m). In particular, the size of such value sets is determined by using finite field theory and known results about crosscorrelation functions.

Original language	English
Pages (from-to)	120-131
Number of pages	12
Journal	SIAM Journal on Computing
Volume	27
Issue number	1
DOIs	https://doi.org/10.1137/S0097539794270352
State	Published - Feb 1998

Keywords

Finite field
Polynomial
Value set

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10.1137/S0097539794270352

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title = "Value sets of some polynomials over finite fields GF(22m)",

abstract = "This paper shows that there is a connection between the crosscorrelation functions of certain binary m-sequences and the value sets of the polynomials xk(1 + x)2m-1 for k ∈ \{±1, ±2,4\}, where x is in the finite field GF(22m). In particular, the size of such value sets is determined by using finite field theory and known results about crosscorrelation functions.",

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year = "1998",

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language = "English",

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publisher = "Society for Industrial and Applied Mathematics Publications",

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AU - Cusick, Thomas W.

PY - 1998/2

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N2 - This paper shows that there is a connection between the crosscorrelation functions of certain binary m-sequences and the value sets of the polynomials xk(1 + x)2m-1 for k ∈ {±1, ±2,4}, where x is in the finite field GF(22m). In particular, the size of such value sets is determined by using finite field theory and known results about crosscorrelation functions.

AB - This paper shows that there is a connection between the crosscorrelation functions of certain binary m-sequences and the value sets of the polynomials xk(1 + x)2m-1 for k ∈ {±1, ±2,4}, where x is in the finite field GF(22m). In particular, the size of such value sets is determined by using finite field theory and known results about crosscorrelation functions.

KW - Finite field

KW - Polynomial

KW - Value set

UR - https://www.scopus.com/pages/publications/11744259023

U2 - 10.1137/S0097539794270352

DO - 10.1137/S0097539794270352

M3 - Article

AN - SCOPUS:11744259023

SN - 0097-5397

VL - 27

SP - 120

EP - 131

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 1

ER -

Value sets of some polynomials over finite fields GF(2^2m)

Abstract

Keywords

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