Irreducible polynomials over GF(2) with prescribed coefficients

Joseph L. Yucas; Gary L. Mullen

doi:10.1016/S0012-365X(03)00092-X

Irreducible polynomials over GF(2) with prescribed coefficients

Joseph L. Yucas
, Gary L. Mullen

Mathematics

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

21 Scopus citations

Abstract

For an even positive integer n, formulas were determined for the number of irreducible polynomials of degree n over GF(2) in which the coefficients of x^n-1, x^n-2 and x^n-3 were specified in advance. GF(2)[x] was used to denote the ring of all polynomials with coefficients in GF(2). Formulas for the number of elements in GF(2ⁿ) with the first three traces specified were also given.

Original language	English (US)
Pages (from-to)	265-279
Number of pages	15
Journal	Discrete Mathematics
Volume	274
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(03)00092-X
State	Published - Jan 6 2004

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/S0012-365X(03)00092-X

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AB - For an even positive integer n, formulas were determined for the number of irreducible polynomials of degree n over GF(2) in which the coefficients of xn-1, xn-2 and xn-3 were specified in advance. GF(2)[x] was used to denote the ring of all polynomials with coefficients in GF(2). Formulas for the number of elements in GF(2n) with the first three traces specified were also given.

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JO - Discrete Mathematics

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Irreducible polynomials over GF(2) with prescribed coefficients

Abstract

All Science Journal Classification (ASJC) codes

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